This was hardly a giant-killing and there was certainly little to choose between the two sides, but as they return to Norfolk to concentrate on the battle for top-flight survival, Nigel Worthington's Premiership strugglers will surely be reflecting on the ones that got away.
For not only did they create more than enough chances to knock Alan Pardew's Championship side out of the competition, but the real twist in the tale came in the form of Harewood - a striker they have been trying to capture for months before switching their attention to Crewe Alexandra's Dean Ashton.
Determined to take no chances against Worthington's side, Pardew had fielded five in midfield, asking Harewood to take a lone role up front in a game that was destined to be dominated by two in-form goalkeepers.
After an edgy start, the Hammers finally started to string a few moves together and Sergei Rebrov saw his curling 20-yarder superbly tipped aside by Robert Green in a show of things to come from the highly-rated shot-stopper.
The fit-again James Walker had replaced Stephen Bywater for a rare outing in the Hammers goal and after smothering the dangerous Darren Huckerby midway through the half he then beat away Jim Brennan's stinging 25-yard shot.
Sloppy passing on both sides saw each team struggling to keep possession and as the chances continued to fall at either end, Green again showed his agility when he palmed Hayden Mullins' low 18-yarder away from the base of his left post to keep it goalless at the break.
Seconds after the restart, a heavy challenge by teenage debutant midfielder Mark Noble led to the crocked Bentley being replaced by Phil Mulryne.
And within moments of their reshuffle, City looked set to take the lead when Huckerby ghosted behind the pushed-up Hammers defence. But after coolly placing his shot beyond the exposed Walker and dancing away in celebration, the red-faced striker was simply mortified to see the ball bounce back off the left-hand post to safety.
Midway through the second half it was Mattias Jonson's turn to hang his head in shame, when Huckerby's throughball left him with just the keeper to beat and this time Walker saved the low, angled eight-yard drive.
At the other end, Green was determined not to be upstaged as he diverted Rebrov's in-swinging, touchline free-kick over his left angle.
However, just when it looked like the tie was heading towards a Carrow Road replay, with just nine minutes remaining, Luke Chadwick burst along the byline and cut back to Harewood who slotted home the winner from six yards to ensure that the West Ham ball goes into Monday's fourth round draw.