A brave second-half City fight-back went unrewarded at Upton Park as West Ham clung onto the points in a pulsating npower Championship contest.
Under the acting management of Jon Rudkin and Mike Stowell following the departure of Sven-Goran Eriksson this week, the Foxes produced an heroic second-half display in front of 3,000 travelling supporters, but came up just short against Sam Allardyce's promotion hopefuls.
At the end of a tough week, the Blues were presented with a huge task as goals from Sam Baldock and Julien Faubert sent the Hammers into the break with a commanding two-goal lead.
And even after pulling a goal back through Andy King on the hour, the Foxes again looked out of the game when Baldock's second restored the Irons' advantage.
But King responded with a spectacular second to set up a grandstand finish, where only the crossbar and the brilliance of Rob Green denied the Foxes a point.
Based on the second-half showing alone, where substitute Steve Howard was an immense attacking presence, the travelling Foxes faithful will have headed out of East London confident that their team are treading the right path.
And as the search for the Club's next permanent manager continues, focus will now switch to Tuesday night's trip to Burnley.
Stowell and Rudkin resisted the temptation to tinker too heavily with personnel following last week's defeat to Millwall - Darius Vassell replacing Michael Johnson in the only change - but they did opt for a different shape.
With Richie Wellens and Yuki Abe holding in front of the back four, Vassell and David Nugent joined Jermaine Beckford in an adventurous three-man attack as City sought to get at their high-flying hosts.
Hammers boss Sam Allardyce welcomed back goalkeeper Rob Green from injury while also introducing impish Baldock to partner big John Carew in attack.
The towering Norwegian cut a frustrated figure in the opening exchanges, persistently penalised for fouls on Sean St. Ledger while competing for the ball in the air and eventually cautioned for his growing crime sheet.
But the former Aston Villa striker played a key role in West Ham's opener on 20 minutes, striding into the right side of the City box onto Mark Noble's pass and chipping a cross to the far post that Baldock merely had to make contact with to score.
After 20 minutes of quiet observance, the Boleyn Ground burst into life and the hosts drew momentum from it as if instantly plugged in to its energy.
A second quickly followed - former Iron Paul Konchesky unable to cut out a fine cross-field ball from Noble and the advancing Joey O'Brien latching onto it before pulling back dangerously from the right. Faubert had time to take a touch before measuring an angled shot across Kasper Schmeichel and inside the far post.
At the end of a difficult week, it was beginning to look a major task for City to lift themselves, but the manner in which they steadied themselves was admirable.
Wellens and Abe fought manfully against Noble and Kevin Nolan in the middle of the park, while Nugent and Vassell did their utmost to provide ammunition for Beckford in the middle.
But the final attacking thrust was just lacking - Beckford a stud's length from converting Nugent's low ball on 27 minutes and Sol Bamba drilling a 20-yarder just wide after juggling his way into space on 32.
They were beginning to show signs of quality. Lee Peltier nut-megged George McCartney down the right before Vassell nearly turned his cross in at the far post and Beckford was denied by Green at close-range after great work from Vassell down the left.
City's attacking intent at the start of the second half was clear, but they were stretched to keep the back door shut two minutes into it - Bamba blocking superbly at the feet of substitute Freddie Piquionne and Konchesky doing likewise from Faubert's follow-up.
The loss of Vassell to injury just before half-time was a blow for the visitors, but the introduction of Lloyd Dyer and Howard soon after brought new energy to the 3,000 travelling fans.
But that was nothing compared with the surge that went through them just before the hour-mark - West Ham unable to clear their lines from a Peltier cross and Wellens delivering from the left for King to head in at the far post.
The response from those behind that goal was truly magnificent, as were the reactions of the man at the other end moments later, as Schmeichel plunged to his left to keep out Baldock's attempt to convert a Collison cross.
King had a big shout for a penalty turned down when he tumbled under the challenge of Winston Reid inside the box as the game started to become stretched.
And that played into the hands of the dangerous Baldock, alert and energetic, who latched expertly onto Piquionne's 71st-minute flick to finish superbly past Schmeichel.
What momentum the Foxes had may have been lost, but they simply refused to lie down and took a leaf out of the West Ham book to draw within striking distance once more just four minutes later.
Schmeichel's booming kick downfield was flicked on by Howard, set brilliantly into the path of King by the intelligence of Nugent and thundered into the top corner by City's midfield ace before Green could move.
It made for a true grandstand finish and only a combination of fortune and fine goalkeeping kept City from the door as the men in blue cranked up the heat in front of their rejuvenated supporters.
With nine minutes remaining, Konchesky crossed dangerously from the right, Howard won a mighty header and Hammers sub James Tomkins turned the ball against his own crossbar.
The hosts breathed again. A minute later and Green had to come to their rescue, diving to his left to repel a powerful Peltier header as St. Ledger crossed from the right.
The home side were well out of their comfort zone and City continued to knock at the door - Nugent angling a shot just wide after picking up the pieces of more damage inflicted by Howard.
But an equaliser proved just beyond their powers and the travelling fans were left to applaud a mighty effort, if an unsuccessful one.
West Ham (4-4-2): Green; O'Brien, Faye (Tomkins 66), Reid, McCartney; Faubert, Noble, Nolan (c), Collison; Carew (Piquionne), Baldock (Sears 88).
Unused subs: Boffin, Bouba-Diop.
Goals: Baldock 20, 71; Faubert 22
Booked: Carew, O'Brien, Faye
City (4-2-1-3): Schmeichel; Peltier, St. Ledger, Bamba, Konchesky; Wellens (c), Abe; King; Vassell (Dyer 46 (Johnson 74)), Beckford (Howard 56), Nugent.
Unused subs: Weale, Pantsil.
Goals: King 59, 75
Referee: James Linington (Isle of Wight)