After leading for so long, Rovers had to settle for just a point in a game of high tension at Upton Park.
Jason Roberts gave Rovers the perfect start when he poked home Brett Emerton's centre after just thirteen minutes.
That stunned the home side, but Rovers failed to increase their advantage, Mame Diouf flagged offside whilst through, then Morten Gamst Pedersen just failed to connect another Emerton centre.
West Ham came out with more purpose in the second half, Demba Ba and Thomas Hitzlsperger going close, but just when it looked like Rovers had weathered the storm they were pegged back, Hitzlsperger drilling the ball through several pairs of legs with 12 minutes to go.
That set up a barnstorming finish, Robbie Kean missing a gilt-edged chance on 88 minutes, before Chris Samba showed true grit and determination to make two last-ditch blocks.
The point doesn't quite see Rovers safe just yet, but they are edging ever closer.
Ahead of the game Steve Kean made three changes from the side that defeated Bolton last time out.
Two of them were enforced with Michel Salgado's knee injury sidelining the Spaniard, whilst a back muscle spasm meant Phil Jones was unable to play. Benjani the third change as he dropped to the bench.
The fit again Junior Hoilett returned to the starting eleven after missing the last three matches, whilst Morten Gamst Pedersen and Mame Biram Diouf returned to start. Nikola Kalinic missed the match after being sent home by the doctor with a high temperature.
Rovers lined up with a wide forward line, Diouf on the right, Hoilett on the left of Jason Roberts, with Morten Gamst Pedersen and Jermaine Jones providing the thrust through the centre.
And it was Pedersen who was in the thick of the action early on. Just two minutes had elapsed when the Norwegian went close, Jones finding Diouf who in turn fed Pedersen but his drilled effort deflected narrowly wide.
Three minutes later and his services were required at the other end, heading off the line to stop a Manuel Da Costa header from a corner kick.
Thirteen minutes in and the deadlock was broken with a superb attacking move from Rovers. Jermaine Jones again powering forward to find Brett Emerton advancing on the overlap and he crossed for Jason Roberts to score with an outstretched boot. Credit to referee Peter Walton for allowing play to continue after Jones had clearly been fouled by Hitzlsperger in the build-up.
Five minutes later it could have been two but Mame Biram Diouf was just offside as he latched onto Junior Hoilett's slide rule pass.
Then as Rovers continued to force the pace, Pedersen was inches away from connecting with another Emerton centre.
But as the first half entered its latter stages, the home side started to impose themselves, Demba Ba glanced a Wayne Bridge cross wide, whilst Jonathan Spector headed tamely at Robinson.
Then a long ball into the Rovers box saw Ba get the better of Chris Samba, but unable to get into a shooting position he fed Freddie Sears, Robinson saving his effort low to his left.
As the clock clicked past added time there was a late scare from a Hitzlsperger corner as Rovers scrambled to clear their lines.
It was a nervy ending to a very nervy first half.
West Ham came out with renewed enthusiasm after the restart, Spector and Hitzlsperger testing the Rovers defence.
But Avram Grant wasted little time in changing his side, Robbie Keane coming on for Luis Boa Morte, but it was Rovers who then enjoyed a spell of pressure themselves.
Chris Samba could only head into the palms of Robert Green from a Pedersen corner, whilst Steven Nzonzi saw his shot beaten away, Hoilett unable to take advantage of the rebound.
The home side then made further changes with Collison and Piquionne coming on, meaning they were employing four strikers. One of those forwards Demba Ba put a low drive narrowly wide.
Rovers made a double change of their own with Roque Santa Cruz replacing Roberts and Keith Andrews coming on for the tiring Hoilett, but it was the back line who were now under pressure.
With twelve minutes to go the pressure eventually told and West Ham were level, Hitzlsperger drilling the ball low through the crowded box and nestling into the corner of the net.
That set up a barnstorming last few minutes, Chris Samba just couldn't get a connection on an Nzonzi flick, whilst Manuel Da Costa was fortunate to escape a second yellow for deliberate hand ball.
All connected with Rovers breathed a huge sigh of relief when Robbie Kean missed a golden opportunity to make it 2-1 to West Ham with two minutes left on the clock, but the Republic of Ireland international striker couldn't score from inside the six yard box, his touch taking the ball away from goal.
Added time saw more drama but captain Chris Samba was in the right place at the right time to make two sensational blocks to deny Ba and then Cole, blocks that might just have just saved Rovers' Premier League status.
WEST HAM: Green (c), Gabbidon, Cole, Hitzlsperger, Boa Morte (sub Keane 55 mins), Spector, Sears (sub Collison 64 mins), Ba, Da Costa, Bridge, Jacobsen (sub Piquionne 64 mins).
Subs not used: Boffin (GK), Tomkins, Kovac, Hines.
ROVERS: Robinson, Emerton, Samba (c), Givet, Olsson, Hoilett (sub Andrews 69 mins), Nzonzi, J, Jones, Pedersen, Diouf (sub Formica 94 mins), Roberts (sub Santa Cruz 69 mins).
Subs not used: Bunn (GK), Rochina, Benjani, Hanley.
Booked: Da Costa, Boa Morte, Spector (West Ham).