The 26-year-old former Nottingham Forest striker blasted a brilliant shot past substitute keeper Brad Jones and into the net after an excellent headed flick-on by Dean Ashton with only 12 minutes left.
The Hammers will now play Liverpool in next month's FA Cup Final at Cardiff's Millennium Stadium.
But Boro will be wondering how they failed to score in a first half they completely dominated.
West Ham looked over-awed as Boro launched wave upon wave of attacks as they showed no sign of tiredness following their recent hectic schedule.
Fabio Rochemback dragged a fourth minute effort wide for Steve McClaren's side before veteran keeper Shaka Hislop got down well to hold Stewart Downing's weak effort.
When West Ham responded Mark Scwarzer dealt confidently with Harewood's acrobatic 15th minute effort.
Frank Queudrue headed over from a good position in the 35th minute as Boro, for all their possession and dominance, struggled to fashion many clear-cut chances.
The Teessiders suffered a major blow just before the interval when Schwarzer had to be replaced by Jones after suffering a fractured cheekbone.
The Hammers must have endured a half-time tongue-lashing from Pardew as they started the second period excellently.
Paul Konchesky's cross was just too high for Nigel Reo-Coker before Ashton headed Yossi Benayoun's 54th minute corner on to the crossbar.
Five minutes later the dangerous Ashton headed another chance straight at Jones before Reo-Coker's drive from a difficult angle flew narrowly wide.
The match appeared to be heading towards extra-time until West Ham scored a magnificent goal.
Ashton headed a long ball on and Harewood latched on to it before blasting an unstoppable shot past the despairing dive of Jones.
In a frenetic finale of numerous substitutions and yellow cards, Boro almost grabbed an equaliser in the fifth and last minute of stoppage time.
The ball fell to the unmarked Chris Riggott inside the penalty area but he dragged his shot horribly wide and, after Hislop had taken the resulting goal kick, referee Mike Riley blew the final whistle.