It was only the second time Ulster have lost on home turf this season as Kevin McLaughlin grabbed the only try of the match while Sexton added a conversion, a penalty and a drop-goal.
The bad news for Declan Kidney was that Ireland centre Paddy Wallace went off with a head injury in the first half but he is expected to shrug off his concussion before the end of the season.
In the other PRO12 match on Friday, Wales' record try-scorer Shane Williams again grabbed a last-gasp try - this time for the Ospreys, who booked their place in the play-offs.
Having scored with the clock beyond 80 minutes in his international farewell against Australia, Williams, potentially making his final appearance at the Liberty Stadium, added the Ospreys' fourth try in a 31-12 win over Newport Gwent Dragons to seal the bonus point.
Williams, 34, may be back one more time at the Liberty Stadium as the five points saw the Ospreys put one foot in a home semi-final, man-of-the-match Ryan Jones and two penalty tries the other scores.