David Healy gave Leeds a rare lead, only for Adam Virgo to equalise just before half-time, but Douglas pounced for the 53rd minute winner after Healy had tried to bundle the ball over the line.
Kevin Kyle hit a Leeds post in injury time but Dennis Wise's men held out.
There was much more purpose and zest from Leeds than they had shown for many weeks as they chased their first win in eight matches. Coventry had been booed off in successive games against Ipswich and Southend and their confidence was at a low ebb.
Wise signed Sunderland left-back Robbie Elliott on an initial month's loan and handed him a debut.
Keeper Neil Sullivan came in for his first start since October, former Maritimo central defender Manuel Rui Marques made a rare appearance and skipper Kevin Nicholls brought much needed power and imagination to the midfield on his return from a three-match suspension.
Coventry boss Micky Adams reacted to Saturday's disappointing 1-1 draw with Southend by replacing Darren Currie, Stephen Hughes and Leon McKenzie with Jay Tabb, Isaac Osbourne and Virgo.
Leeds were much quicker to settle and they scored the first goal for the first time in nine games. With 15 minutes gone, Coventry failed to clear Eddie Lewis' corner from the right, Healy controlled the ball beyond the far post, turned and drilled his shot into the bottom far corner for his seventh goal of the season.
Nicholls tried his luck with a powerful 30-yard drive which was only just too high.
Coventry at last began to show their attacking teeth and, after Virgo had wasted a good chance by shooting into the side-netting, Sullivan had to make a point-blank save to deny Kyle an equaliser.
Robbie Blake struck Coventry's bar with a 25-yard free-kick after Lewis had been brought down by Andy Whing in full flight, and the bar foiled Leeds again from Lewis' free-kick after the lively Nicholls was fouled by Osbourne.
Despite taking a back seat for so long, Coventry equalised in the 43rd minute. Marques made a weak headed clearance, Kyle whipped the ball into the goalmouth from the left and Virgo gave Sullivan no chance, shooting home from six yards.
However, Leeds' winner arrived when Lewis made one of his many runs, Healy was blocked by keeper Andy Marshall and Douglas lashed the loose ball into the net.