Goals from Billy Mehmet and Marce Collington were enough to seal the points against the Sky Blues, who provided tough opposition for the Hammers.
After a fairly even opening half an hour, Hammers finally made the breakthrough 10 minutes before half-time when Darryl McMahon's fierce shot was parried and Mehmet was on hand to convert the rebound.
However, the visitors didn't allow the goal to dent their confidence and enjoyed plenty of possession in the second half without ever really threatening the Hammers' goal.
With 10 minutes remaining, Collington came on for his first taste of under-19s football this season and within five minutes had notched his first goal at this level, when he received a pass from Phil Lumsden and slotted home.
That sealed the victory for Hammers and left coach Tony Carr relieved and satisfied.
"It was a very tough game," he said, "and we were made to work very hard for our victory.
"Coventry packed the midfield and had a lot of possession, although they never really looked like scoring.
"I felt it was very important that we scored the first goal and things were more comfortable after we did that, but you can never be sure with a 1-0 lead and it was nice to wrap up the victory in the last five minutes.
"It was a very satisfying result and gets us back to winning ways."
Team: Jackson, McClenahan, Tattam, Ferdinand, Ward, Lumsden, Allen (Khan 60), McMahon, Pearson (Collington 80), Mehmet, Carrick. Subs unused: Morgan, Fletcher, Laws.
*Kevin Keen's under-17 side were not in action.