Somma netted an equaliser at Hull on Tuesday night and was on target again here at a time when his side desperately needed a goal to put Coventry, now without a league win in 10, deservedly behind.
United had missed a string of chances by the time Somma struck and, like the majority of his 10 goals from as many starts this season, it was little more than a tidy finish from inside the box but it did the job for Simon Grayson's side, who have now tasted defeat just once in 17 Championship outings.
And while it was Somma's goal that won the points, it was the outstanding Robert Snodgrass who drove Leeds to the win ahead of his expected Scotland debut on Wednesday night.
The winger had a hand in laying on numerous chances for his team-mates, who, until Somma found his range, were more than generous in front of goal.
Having recovered a two-goal deficit to draw at Hull on Tuesday night, it was apparent that Leeds were eager to start better today and Somma could have given them a fourth-minute lead had he been able to keep a snap-shot down after a Snodgrass knock-down.
Somma's miss would set the tone for the majority of the first half, as, after Richard Wood went close for City when his close-range hit was deflected wide by Luciano Becchio, Leeds assumed complete control and contrived to miss a hatful of chances.
Thirteen-goal top-scorer Becchio was the worst culprit for Leeds, twice missing from three yards, while winger Max Gradel was also culpable.
With 19 minutes gone, a quick release from Kasper Schmeichel sent Paul Connolly racing down the right, he found Snodgrass but his cross was stabbed wide by Becchio with goalkeeper Keiren Westwood nowhere to be seen.
Leeds continued to apply the pressure and two minutes later Gradel scorched a shot wide after breaking clear with a jinking run, and the Ivorian was wasteful again shortly after, slicing over on the break when he had team-mates queuing up to be played in.
Despite his profligacy, Gradel was running the Coventry defence ragged and, after his break, George McCartney raced into the box and squared for Becchio who miscued across goal, before Leeds had a penalty appeal turned down when Bradley Johnson's cross appeared to hit Jordan Clarke's arm.
Gradel was unable to turn Snodgrass' menacing cross beyond Westwood as the second half started as the first had ended, before Somma grabbed the goal Leeds had been threatening ever since his early chance.
Snodgrass was the key architect, winning the ball in midfield and creating space before playing in Gradel, whose cross was played back across goal by Jonny Howson from where the waiting Somma gave Leeds a 56th-minute advantage.
The goal could quite easily have meant little for Leeds a minute later, though, when Lucas Jutkiewicz snapped a drive over on the turn.
The outstanding Snodgrass then drew a flying save from Westwood, while at the other end, Aron Gunnarsson placed a low drive just wide of Schmeichel's left-hand post.
Somma was denied a second - a 25-yard lob over Westwood - by the offside flag, and Alex Bruce scraped wide as Leeds pressed for a clincher, but they held out under minimal Coventry pressure, with the visitors only threatening when Leigh Bromby deflected Clive Platt's shot over.