The hosts took the lead against the run of play just before half-time through Clark Carlisle's header.
Julian Joachim made amends for a first-half miss by pouncing on a rebound from close range to score his first goal for Leeds against his former club.
Coventry had Louis Carey sent off for a second booking before Frazer Richardson's close-range finish.
Coventry manager Peter Reid:
"It is important that you defend properly, especially from
set-pieces but we didn't do that.
"I don't think the scoreline reflected the game
but we paid for our mistakes.
"I thought Louis Carey was a little bit unlucky. I won't argue with the decision
but there were a few tackles that could have resulted in a booking. His bookings
were a bit harsh."
Leeds: Sullivan, Kelly, Carlisle, Butler, Crainey, Richardson,
Wright, Walton, Pugh, Joachim (Ricketts 90),
Deane (McMaster 85). Subs Not Used: Carson, Spring, Duberry.
Booked: Pugh.
Goals: Carlisle 40, Joachim 71, Richardson 90.
Coventry: Shearer, Carey, Shaw, Leacock, Staunton (Barrett 79), Doyle, Sherwood, Hughes, Wood (Whing 79), Morrell, Johnson (Suffo 45). Subs Not Used: Steele, Gudjonsson.
Sent Off: Carey (72).
Booked: Carey.
Att: 26,725.
Ref: P Robinson (E Yorkshire).