Hull in midweek.
Coventry arrived without a league win since early December, but they had the first chance when Richard Wood fired wide from close range after United failed to clear a corner.
There were a few lively early challenges with both Robert Snodgrass and Carl Baker being on the wrong end of a couple during the first 15 minutes.
It wasn't the most entertaining opening, but Leeds almost nicked the lead on 18 minutes. Snodgrass delivered a good cross from the right and Luciano Becchio stabbed his shot just wide of the mark.
Moments later, Max Gradel used his trickery to cut in from the left, easing past Jordon Clarke brilliantly, but his shot was just wide of the mark.
Within two minutes, Gradel tied Clarke in knots again before delivering another effort which was just wide.
Just before the half-hour, Gradel again instigated an attack that saw Becchio turn a George McCartney cross inches wide of the upright.
United continued to take the game to Coventry, Gradel and McCartney were linking up superbly, and Bradley Johnson felt he had claims for a penalty when a cross appeared to hit the hand of a visiting defender.
McCartney also made a timely clearance at the other end shortly before the break as Coventry mounted a rare raid forward.
But it was the visitors who were defending again at the end of half, first clearing a Snodgrass then blocking a Paul Connolly delivery.
United also started the second half on the front foot, and again Coventry had some early defending to do.
Coventry's rearguard was eventually broken on 55 minutes, courtesy of Somma. Gradel supplied the cross from the right, Jonny Howson knocked into back into the box, and Somma converted from close range.
Moments later, Snodgrass went close for Leeds when Keiren Westwood pulled off a great save, but Coventry did fashion a half-chance on 64 minutes when Aaron Gunnarsson went close.
Somma thought he had put the game beyond doubt on 72 minutes when he latched on to a flick-on to deliver a superb chipped finish - but he was denied a second goal by an offside flag.
Alex Bruce was next to go close when Coventry failed to clear a corner, and the central defender turned on the edge of the box with a great strike which went just wide.
Tempers flared with 10 minutes remaining when Clarke was booked for Coventry after a late challenge on Gradel.
Both Neil Kilkenny and Billy Paynter were brought on as the game headed towards its closing stages, and barring one great save from Schmeichel to deny Clive Platt, the visitors offered little in the way of trouble.
Snodgrass almost added a second goal in stoppage time, but one proved enough as United maintained the pressure on the leading pack in the Championship.