But it came at a cost - having lost Roger Wilson pre-match to a back spasm, Iain Henderson (hamstring), Darren Cave (shoulder), Peter Nelson (foot) and Dan Tuohy (ankle) all suffered injuries during the game.
Kiss said: "It was a pretty special win when you take into account we lost Roger (Wilson) before the game and then the injuries meant players were playing out of position.
"We will have to assess the injuries, but a couple of them may be long term.
"The boys will rebound, and we have enough resources so we will try not to get too downhearted about it."
A penalty try and a Rory Scholes score had the Irish province 14-0 up within ten minutes and they held that advantage until half-time, as they looked to end a three-match losing streak against Scottish opponents.
Cornell du Preez touched down for the visitors early into the second half but failed to close the gap as Ulster recorded a fifth win of the campaign.
Kiss added: "It is a credit to the boys that they upped the ante and put speed into the game because that is something that Edinburgh try to take away from you and they did that well, which is why we ended up with the 14 points - which was very valuable in the end.
"I think we left a couple [of tries] out there and were denied one which gave them the bonus point, which is a disappointment in some ways.
"But you can't always have things your own way and you have to be a team that can handle all conditions.
"You have to be able to play different ways to mix it with the best in the business in those kinds of environments to test yourself to be able to go to the next level, so there were positives."
To buy tickets for the GUINNESS PRO12 Grand Final click here. Also follow us on Facebook, join the conversation on Twitter, sign up to our YouTube channel for extensive match highlights and sign up for our newsletter for regular updates on the GUINNESS PRO12.
63x46.png){kind=logo}