Cliftonville moved to within five points of Premiership leaders Crusaders thanks to this Solitude victory.
The hosts seized control after a tight opening and Stephen Garrett saw his shot hit the woodwork before the lively Chris Curran fizzed just over.
Martin Donnelly got the final touch from a goalmouth scramble to put the Reds ahead seconds before the break.
Reds skipper George McMullan fired wide and Andy Coleman saved from Donnelly as Cliftonville secured a deserved win.
What they said
Cliftonville manager Gerard Lyttle said: "I don't think we played as well as we usually do although we have seven players out.
"We were a bit slower than normal in the first half but we got our game sorted and flowing and we scored the goal at a good time."
Dungannon boss Rodney McAree said: "In the first half we were below par and our ball retention was poor, but the second half was much better."