It is the first time this season that they have strung three league wins together and will come as a welcome boost to their promotion hopes.
Gillingham played the better football as the half went on, but failed to make their possession count.
West Ham struggled to deal with Nicky Southall's crosses with Mathew Jarvis and Andrew Crofts coming close after being set up by the winger.
They were made to pay for their misses after 13 minutes when Harewood scored his 16th goal of the season.
Matthew Etherington scampered down the wing and sent over a dangerous ball across the face of the goal and Harewood darted through a static defence to tap the ball home from just six yards.
The home side almost drew level midway through the half when Crofts combined with Southall again only to see his piledriver from the edge of the box tipped around the post.
A mixture of poor finishing and last-ditch tackles prevented the home side going into the break level with the West Ham defence at sixes and sevens.
Their attacking play left them open for a quick counter-attack and Bobby Zamora should have scored on the half-hour when he tamely headed the ball into Steve Banks' arms when unmarked from 12 yards.
Gillingham continued to press after the break and came close to scoring when Paul Smith curled one just over the bar for the home side from the edge of the box.
And just minutes later Harewood had his powerful volley from 30 yards brilliantly tipped round the post by Banks at the other end.
Second-half substitute Teddy Sheringham almost doubled West Ham's lead when he rattled the bar with a curling 25-yard free-kick on 74 minutes.