But the Warriors, who had led the GUINNESS PRO12 for much of the season, ran in four fine scores after the break, Finn Russell notching a pair in between efforts from Stuart Hogg and Richie Vernon to ensure they finished on the league's summit.
And with the home semi-final secured against the same opponents for next weekend, Kellock is calling on his side to go all the way before he sets off into the GUINNESS PRO12 sunset.
"We knew what we had to do. Ulster are a very good team and the conditions were such that we had to play two different halves," the 33-year-old said.
"To keep them to a four-point lead at half-time was great and we came out and played some great rugby, especially in the last 20 minutes.
"They had a lot of big names on their bench but I thought our bench was absolutely superb.
"Now we need to improve on what we did last year and push as hard as we can to not only win this semi-final but to go on and take the title."
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