Centre Paddy Jackson also scored 16 for Ulster and scrum-half Paul Marshall nipped in but the play-off chasers were unable to match Sunday's Heineken Cup heroics.
After winning their last RaboDirect PRO12 game 27-19 away to Newport Gwent Dragons Connacht looked a buoyed team and maintained their good form.
Nikora put Connacht into an early 8-0 lead, first from a penalty and then from a try as he slipped in between Robbie Diack and Adam D'Arcy to go over next to the posts.
But after Ronan Loughney's sin-binning, Ulster dragged themselves back as Jackson took over the kicking duties from Ian Humphreys who was off target with two early penalties. Jackson, 20, picked the baton in style by driving over two penalties to pull the visitors back into contention at 8-6 down.
But captain Duffy opened the gap again on the half-hour when Kyle Tonetti released him down the right wing and he cut past Stefan Terblanche for a clinical score.
Marshall picked up from the base of a ruck and dived over for Ulster's first try of the game as the Heineken Cup semi-finalists finished the first half strongly.
Jackson landed the conversion and followed it with a penalty just before the break to put Brian McLaughlin's men 16-13 in front.
But Connacht came out at a rate of knots in the second half and with only three minutes gone John Muldoon cheekily off-loaded to O'Halloran who shot off past Ruan Pienaar to dive over in the corner.
Nikora slotted over the conversion from a tight angle to put Connacht back in front.
The see-saw nature of the game continued and Ulster hit back as Jackson drove over from close range after some good forward pressure although he could not convert his own score.
But the nerveless Nikora proved to be the difference as he slapped a penalty over on 60 minutes to put the Galway side back in front for the final time.
However, the tension was too much for some as Michael Swift and Lewis Stevenson were sin-binned for fighting.
But Connacht held firm in the closing stages and when Ulster replacement Ali Birch was yellow-carded, Nikora capped off his day in fine style to score the final penalty and bring Ulster back down to earth with a bump.
|Connacht Rugby Score Card|
|Ulster Rugby Score Card|