ALBION and Peterborough will have to do it all over again after Craig Mackail-Smith's dramatic late equaliser earned the League One high-fliers a replay.
Jonas Olsson's first Hawthorns goal in the 64th minute appeared to have booked the Baggies' passage into the FA Cup fourth round for the fourth time in five years.
But Mackail-Smith kept Posh's cup dreams alive by scrambling home an 87th-minute leveller - his 18th of the season.
It was no less than Darren Ferguson's side deserved after they gave the Barclays Premier League hosts a real run for their money.
Although the Baggies' concerted second-half pressure warranted a goal, keeper Scott Carson had a busier afternoon than he would have wanted and had to pull off two smart saves to deny Aaron Mclean and George Boyd while Mackail-Smith hit the bar.
Carson's England gloves rival, Joe Lewis, was also busy at the other end and it was largely thanks to his hard work Posh kept Albion out until just past the hour mark.
The Baggies now face a third cup trip to London Road inside 17 months after knocking Posh out of both the Carling and FA competitions last term.
Mowbray made two enforced changes for this third-round tie, with fit-again Robert Koren and Carl Hoefkens coming in for James Morrison (groin) and Gianni Zuiverloon (knee).
New loan signing Jay Simpson was named among the subs.
Albion enjoyed plenty of possession during a scrappy opening to the game but failed to seriously threaten Lewis' goal.
The closest they came was in the second minute when Chris Brunt saw his fierce free-kick clip the Posh wall and loop over.
Albion's next effort on goal came on 13 when Brunt exchanged a neat one-two with Roman Bednar before volleying over from 20 yards.
Brunt was in the thick of it again four minutes later when Lewis' attempted punch failed to connect with the midfielder's in-swinging corner. Luckily for the ex-Norwich keeper, the ball curled just wide of the far post.
The visitors had barely crossed the halfway line - but almost snatched a 20th-minute lead.
Mackail-Smith outmuscled Leon Barnett as they contested Charlie Lee's high punt into the Baggies half and the United striker advanced into the box before seeing his 15-yard curler cannon off the bar.
As Peterborough grew in confidence, Albion had to defend four successive corners - but their backline stood firm.
The Baggies were soon back on the attack and centre-half Craig Morgan had to pull off a stunning last-ditch interception to prevent Borja Valero's through-ball finding Luke Moore.
But it was United who recorded the game's first shot on target.
Carson had to produce a fine reflex save to deny Mclean's 12-yard volley from Chris Whelpdale's pull-back.
Albion had struggled to find any real rhythm thus far and Brunt had to resort to two more long-range efforts, with his first being blocked by Morgan and his second screwing wide of the far post.
The Baggies produced their best moment of the game in the 41st minute. Valero and Koren bamboozled the Posh defence with a deft one-two before the Spaniard saw his centre headed inches wide of his own goal by Gabriel Zakuani.
From Brunt's ensuing corner, Lewis could only punch as far as Koren but the Slovenian was well off target with his instinctive ten-yard volley.
Peterborough had the final effort of the half. Whelpdale cut in from the right and saw his 20-yarder gathered by Carson at the second attempt.
Mowbray made a change at half-time, bringing debutant Simpson on for Koren.
Albion pushed Posh back inside their own half at the start of the second half but Greening failed to trouble Lewis' goal with a couple of long-range efforts.
Moore went much closer in the 55th minute.
The ex-Villa striker did brilliantly to control Brunt's high ball inside the area and take it inside Morgan in one movement, but he lost his balance and saw his stab goalwards blocked by the onrushing Lewis.
Seconds later, Lewis had to pull off an even better save to push away Greening's stinging volley from just outside the box.
Simpson smashed the rebound goalwards from the tightest of angles and the Brummie Road End rose in unison to celebrate a 'goal' as Lewis grasped the ball on the goalline.
But referee Kevin Friend ruled the United keeper had prevented it creeping over.
Lewis was called into action again on 59 when he dived low to his right to clutch Valero's 18-yard drive.
Peterborough earned some respite from the Baggies siege when Boyd tested Carson with an awkward 30-yard shot. The England keeper parried the ball before gathering at the second attempt.
But the Albion pressure had been mounting and Mowbray's men finally broke the deadlock in the 64th minute.
Olsson used all of his 6ft 5in frame to tower above the Peterborough defence and head Greening's corner inside the far post.
Peterborough weren't ready to throw in the towel just yet and Boyd caused real concern when he jinked inside Simpson and Hoefkens before firing just wide from 20 yards.
And Albion had a real let off on 68 when Mackail-Smith, with the goal at his mercy, somehow failed to connect with Boyd's centre, allowing the ball to drift harmlessly wide of the far post.
But after a lull in the game, Peterborough found their second wind and snatched a dramatic 87th-minute equaliser.
Mclean made room on the right-hand edge of the box to squeeze in a cross and Mackail-Smith slotted past Carson from close range.
The drama wasn't over yet either. Mclean exchanged passes with former Walsall midfielder Dean Keates in the last minute before dragging his shot just wide of the near post, with Carson beaten.
Lewis then came to Posh's rescue in stoppage time when he parried Marek Cech's strike before Zakuani cleared.
ALBION (4-4-2): Carson; Hoefkens, Barnett, Olsson, Cech; Koren (Simpson HT), Greening, Valero, Brunt; Moore (Dorrans 70), Bednar (Beattie 76). Subs not used: Kiely (gk), Robinson, Kim, Donk.
PETERBOROUGH (4-4-2): Lewis; Martin, Morgan, Zakuani, Lee; Whelpdale (Batt 75), Coutts, Keates, Boyd; Mclean (Torres 90+3), Mackail-Smith. Subs not used: McKeown (gk), Westwood, Blanchett, Green, Andrews.
GOALS: ALBION - Olsson (64). PETERBOROUGH - Mackail-Smith (87).
BOOKINGS: none.
REFEREE: K Friend (Leicestershire).
ATTENDANCE: 18,659.
ALBION STARMAN: Jonas Olsson.
PIC: TOWER OF STRENGTH...Olsson celebrates his goal with Greening
