The Blues led 14-6 at half-time at Murrayfield thanks to Michael Paterson’s try.
Edinburgh fought back and claimed a try of their own through WP Nel but Rhys Patchell booted the Blues victory.
“In the past we might have lost that won but it just shows how far we have come this season,” said Blues director of rugby Phil Davies
“The attitude and spirit was outstanding – it’s a great credit to the players.
“Patchell and Lewis Jones at half-back, and Alex Walker when he came on, did a great job. They moved the ball nicely and kicked very well.
“There’s still a lot to play for in the PRO12. We want to win every game and “Connacht at home is a massive game for us before we go away to Glasgow – there’s 10 points on offer.
“You never know what will happen and if we win those matches we will be in a much stronger position.”
Gregor Hunter missed two early shots at goal and was punished for his inaccuracy as Patchell fired the Blues into a 6-0 lead.
The two fly-halves continued to exchange shots at goal and the Blues stretched their advantage with Paterson’s try.
Patchell ghosted past two defenders to send the Kiwi over the whitewash minutes before the interval.
Nel drove over from close-range early in the second-half and Hunter, and his replacement Harry Leonard, kept the scoreboard ticking.
But Patchell nailed his fourth penalty on 66 minutes to put the Blues back in front and Edinburgh never recovered.
