The afternoon had started badly when Shane Long had put the away side in front after just three minutes, and things did not look like improving in a below par first-half display that saw Malouda replace Salomon Kalou after half an hour.
There must have been stern words at half-time from Andre Villas-Boas on his home debut and Chelsea came out improved in the second period, Anelka quickly evening the scores up with a hard, low finish from inside the area, and after a couple of scares at either end, it fell to Malouda to wrap up a first win of the campaign and three important points against a capable opposition.
Jose Bosingwa's assist for the winner, picking the ball up deep on the right and running in between two West Brom challenges before delivering the perfect low cross to his team-mate arriving at the far post.
Injury to Petr Cech had given Villas-Boas his main selection problem in midweek, and after assessing the options available opted to go with his compatriot Hilario in goal, with Ross Turnbull on the bench.
Elsewhere Anelka, a substitute against Stoke last week, was drafted in to replace Florent Malouda, the Frenchman beginning the afternoon on the right of the front three, with Kalou switching to the left. Fernando Torres continued in attack after his impressive showing at the Britannia last weekend.
West Brom, beaten by a late Manchester United winner at home last weekend, were unchanged, which meant powerhouse Somen Tchoyi partnering new boy Long in attack. Last season's top goalscorer Peter Odemwingie was on the bench following injury. Captain Chris Brunt, a left-footed wide man, was on the right flank, his height possibly seen by manager Roy Hodgson as a weapon against the diminutive Ashley Cole.
Chelsea were wearing black armbands to mark the passing of Stan Willemse, a member of our 1955 championship-winning side.
The new manager's home debut could not have started worse, his side struggling for any rhythm and falling behind to an avoidable goal inside five minutes.
The Blues needlessly surrendered possession, leaving Alex one on one with Long, a battle the Brazilian would have expected to win, but when he lost his footing the Irishman was given a clear run on goal, and calmly slotted past Hilario for his second goal in as many games since signing from Reading.
It was 13 minutes before Chelsea showed any invention, Kalou cutting in off the left and firing high on his right, and then Anelka looping a header straight at Ben Foster either side of a Paul Scharner drive beaten behind by Hilario at his near post.
Long and Tchoyi almost combined to double the visitors' lead but the scorer overhit his square pass for his strike partner. Villas-Boas was visibly unimpressed with his side's creativity, and so just after the half-hour made his first change, Malouda on for Kalou in a straight swap.
Chelsea's next attempt came from the left side, but it was from defender Ashley Cole rather than the substitute. The England man strode forward five minutes before half-time and unleashed a powerful, rising drive that was arrowing for the top corner until Foster put fingertips to it to divert it behind for a corner, which came to nothing.
Three minutes later Chelsea should have had a penalty. A loose ball was pounced upon by Anelka, who arrived a fraction of a second before Foster and toed the ball past the goalkeeper before being brought to the ground. Goal kick said referee Lee Mason.
He did blow his whistle moments later when Torres was brought down on the edge of the area, but Alex's free-kick, deflected off Mikel, was well held low down by the goalkeeper. There were at least signs at last of Chelsea coming to life, and Foster would be brought into action once more before the break when he scrambled across his goal to deny another Anelka header.
It took seven second-half minutes for Chelsea to level the scores.
Lampard was adjudged to have been cleanly tackled inside the box but when it fell loose to Anelka on the right, the Frenchman came inside, worked the ball back on to his favoured right side and shot low from an angle past Foster and into the far corner.
Things suddenly looked a lot brighter, and within a couple of minutes Lampard had forced a corner with a deflected effort and Malouda had seen a half-volley cleared from inside a busy six-yard box.
Suddenly the blue shirts were finding space. Lampard played in Anelka, who was denied by Foster's leg, and from the rebound Jonas Olsson blocked Malouda's volley.
Stamford Bridge was louder too, anticipating a second home goal. On came Drogba in place of Torres.
Chelsea were by now dominating possession, the midfield all playing further up than they had in the first half, but that was at times leaving the defence, shorn of Cole and Bosingwa who both like to get forward, a little exposed to counter-attacking.
Long and Tchoyi were still posing problems. Just after the hour the Cameroonian bent an effort wickedly towards the far corner, Hilario just tipping it around the post. The Portuguese was letting nobody down with his performance.
Back at the Matthew Harding End, Drogba poked a Cole cross the wrong side of the post and Anelka shot over the bar. Villas-Boas replaced Alex, who had struggled to cope with West Brom's forwards, with Ivanovic.
The Serbian, playing in the centre of defence, was allowed to come forward with the ball 21 minutes from time, and his cross found a free Drogba, but the forward could not connect and the chance was wasted.
Cole brought another low save from Foster as the Baggies crammed 11 men behind the ball, there was a penalty appeal against an Olsson handball, and then Lampard flicked a volley just over as we approached the final 10 minutes.
A rush of blood to the head from Foster allowed Anelka the chance to shoot on a Chelsea break, but he curled into the side netting. Time was running out.
Then it came.
Bosingwa looked to have too much on in order to get the ball into the area, but he skipped between two defenders with confidence and squared low across the box between goalkeeper and defence. It was perfectly weighted, and there was Malouda at the far post to put his side in front for the first time.
The visitors were not beaten yet though, and should have had an equaliser. Substitute Odemwingie, on for the tired Tchoyi, was left unmarked at the far post and was found by Steven Reid's deep cross. With the whole goal to aim for, he found the legs of a grateful Hilario, passing up his side's last opportunity of the game.
That brings Chelsea back to winning ways after four in the league without maximum points, and we now have a week to prepare for the visit of Norwich City next Saturday.
Chelsea (4-3-3): Hilario; Bosingwa, Alex (Ivanovic 66), Terry (c), Cole; Ramires, Mikel, Lampard; Anelka, Torres (Drogba 59), Kalou (Malouda 34)
Unused subs Turnbull, Ferreira, McEachran, Benayoun
Goals Anelka 52, Malouda 82
Booked Lampard 33, Terry 89
West Bromwich Albion (4-4-2): Foster; Reid, Tamas, Olsson, Shorey; Brunt (c), Scharner, Mulumbu (Dorrans 86), Morrison; Tchoyi (Odemwingie 74), Long
Unused subs Fulop, Cech, McAuley, Jara, Cox
Goals Long 4
Booked Tamas 6, Mulumbo 44, Olsson 59, Odemwingie 90+1
Referee Lee Mason