Hammers entered their first taste of cup football this season on the back of Saturdays morale-boosting win at Crewe, when Teddy Sheringham's double strike sent Alan Pardew's men on their way to all three points at Gresty Road.
However, mindful of a busy Bank Holiday weekend coming up, the Hammers boss took the decision to rest his veteran stand-in skipper, along with Hayden Mullins, Matthew Etherington, Anton Ferdinand and Steven Bywater.
That meant debuts for young defenders Elliott Ward and Trent McClenahan, goalkeeper James Walker, while Chris Cohen and Sergei Rebrov were also handed a place in the starting line-up.
One regular to retain his place was Harewood, and it was the burly striker who made an early breakthrough for Hammers after 11 minutes.
After a dangerous Southend cross had been cleared, Nigel Reo-Coker escaped on the break and stormed at the heart of the Shrimpers defence before releasing the Harewood, who slotted coolly past Bart Griemink for his first goal of the season.
The visitors should have levelled just a few minutes later, but striker Drewe Broughton planted his header wide from just six yards out.
That was the closest they came before snatching an equaliser before the break, but Steve Tilson's men produced a spirited display in the second half that almost earned them the chance of causing a possible extra-time upset.
Skipper Kevin Maher twice went close with long-range efforts, while Mark Bentley will be wondering how he managed to blaze a simple chance over the bar from eight yards out.
Sheringham made a late substitute appearance, along with another young debutant, Mark Noble, but in the end his class wasn't needed as the Hammers held on to their slender lead and rounded off the evening when Harewood broke away to fire home his second of the game in stoppage time.