First-half goals by Bobby Zamora and Carlos Tevez brought renewed hope to an East End helplessly resigned to relegation but, with the Hammers needing a victorious run of title-winning proportions, it remains to be seen whether Alan Curbishley's boys can still burrow their way to Premiership safety.
With his strugglers rooted in 19th spot, Curbishley had enjoyed outrageous fortune last time out at Blackburn, after substitute Zamora gave his side a rare victory with the goal that never was.
But with the Hammers' match-winner duly promoted to the starting line-up in place of Marlon Harewood, there was absolutely no doubt that Zamora's opener had crossed the line this time around.
Indeed, just two minutes were on the clock when West Ham's top-scorer sent his unstoppable eight-yarder ripping into the net, after Tevez's right-wing cross was deflected into his path by the luckless Emanuel Pogatetz.
Gareth Southgate had earned widespread condemnation from all the Premiership strugglers when he fielded a weakened side against Manchester City ahead of his side's FA Cup quarter-final replay at Old Trafford.
But following their controversial exit at the hands of Manchester United's Cristiano Ronaldo, 12th-placed Boro only made two enforced changes as the injured Julio Arca and suspended Lee Cattermole were replaced by Stuart Parnaby and Fabio Rochemback.
Yet apart from Mark Viduka's hopeful overhead kick and George Boateng's stinging 18-yarder, the Teessiders barely threatened and, after Mark Schwarzer saved well from Matthew Etherington and Tevez, Curbishley's half-time team-talk was made even easier, thanks to his Argentinian ace.
Again, a Boro defender played an unwitting hand in the West Ham goal. This time, George McCartney's hanging, 45th-minute cross bounced off the knee of Andrew Taylor and Tevez gleefully fired his third goal in as many games into the roof of the net from six yards.
Certainly, the teasing and tormenting Tevez was keeping the beleaguered Boro defence on its toes and, on the hour, Pogatetz was booked after finally chopping the aggravating Argentinian onto the turf at the third attempt.
Sadly for Southgate, though, that was a rare moment of fight and, in a wind-blighted second period, below-par Boro never looked like repairing the first-half damage inflicted by a West Ham United side finally fighting for their lives.