The South Yorkshire club also ended a five-game losing run with this crucial victory and now sit in ninth place.
It was a much-needed result as they attempt to avoid being dragged into a Championship relegation battle.
But with a visit to bottom-placed Hartpury on Saturday before hosting Richmond, who sit tenth, Doncaster could well be on the way to fulfilling that aim by the end of the month.
At Coventry, Knights led 7-5 at the interval, but were 17-10 down approaching the hour mark.
However, Ollie Stedman came up with a try that Dougie Flockhart converted to level the game.
Winger Flockhart, recalled after injuries to Paul Jarvis and Curtis Wilson, then showed his composure with two more penalties to clinch it.
He finished with a haul of 13 points while full-back Stevie McColl, who had also earned a recall after Doncaster’s loss to Yorkshire Carnegie, scored their other try.
Griffiths said: “It has been a long time coming and we’ve kept getting close in games.
“But it was an outstanding performance from the boys. What pleased me most was the fight and togetherness; we showed everyone that Doncaster Knights are still around and we’ve players that want to win and do well for the club.
“Now we have to back that up; we can’t take our foot of the gas.”