Replacement tighthead prop Nicol scored the clincher in the 77th minute as the Warriors came out on top 36-33 at Scotstoun.
After the victory – gaining a measure of revenge for last week’s 50-19 loss to the same opponents in Belfast – Rennie said: “I’m happy with the win.
“They are a good side Ulster so it was a real arm wrestle and could have gone either way.
“They asked a lot of questions of us and while a lot of our defence was a big step-up from last week’s there are still areas around connection and trust where we have to be better defensively.”
Rob Herring and Rob Lyttle both scored tries early on as Ulster went 12-0 up before a good Warriors spell put them 17-12 up at half-time.
A penalty try was followed up by an effort from Rory Hughes and then Brandon Thomson kicked a penalty to put them ahead.
Stuart McCloskey scored Ulster’s third try just after half-time before Johnny Matthews went over for Glasgow.
A penalty try then went Ulster’s before man of the match Glenn Bryce’s converted score put the home side up 31-26 with 19 minutes to go.
James Hume’s converted try six minutes later again put the men from Belfast ahead before the winning try came from Nicol.
Glasgow start the Guinness Pro14 season away to the Cheetahs in South Africa on 27 September.