Gary McSheffrey put the home side in front with a low shot after being found by Dele Adebola, who held off three defenders before setting him up.
But Leeds were given the chance to pull level when Andrew Whing was adjudged to have handled after 88 minutes.
Healy made no mistake as he drilled the ball low into the bottom corner for his 12th goal of the season.
"We had two chances to clear the ball in the run-up to the incident which we did not do and that disappoints me."
"Coventry defended stoutly and their keeper made several good saves, but credit to the lads as they kept going.
"At one point we were 17 points off automatic promotion but now it is only four."
Coventry: Fulop, Whing, Page, Shaw, Hall, Scowcroft, Hutchison, Doyle (Thornton 84), McSheffrey (Impey 79), John, Adebola.
Subs Not Used: Ince, Williams, Morrell.
Booked: McSheffrey, Hutchison, Page.
Goals: McSheffrey 26.
Leeds: Sullivan, Kelly, Butler, Kilgallon, Crainey, Douglas (Moore 74), Derry, Miller, Blake (Healy 61), Hulse, Lewis.
Subs Not Used: Bennett, Einarsson, Bakke.
Goals: Healy 88 pen.
Att: 26,643
Ref: C Oliver (Northumberland).