A brilliant start helped Connacht get the better of Ulster as both sides returned to action in an entertaining Pro14 encounter in Dublin.
Connacht looked by far the sharper side as the teams re-emerged from a near six-month break, with first-half tries from John Porch and Kieran Marmion giving them a deserved half-time lead.
Jacob Stockdale and Nick Timoney crossed for an improved Ulster after the break but Bundee Aki and Jack Aungier powered over to secure Connacht's bonus-point win.
The result is inconsequential as far as qualification for the semi-finals is concerned, with Connacht already out of contention and Ulster assured of their place in the last four.
Regardless, it was an impressive showing from the western province, while Ulster will hope to shake off any remaining rust before they enter the knockout stage of the competition.
Fast start aids Connacht win
After the prolonged break, both sides could have been forgiven for taking some time to rediscover their best form, but Connacht impressed from the outset at an empty Aviva Stadium.
Porch collected Jack Carty's inventive overhead pass on 12 minutes to score the game's opening try as Connacht's back punched holes in Ulster's defence at will.
Eleven minutes later they crossed again as debutant Alex Wootton delivered a magnificent one-handed offload to Porch whose infield grubber kick was smartly collected by Marmion.
Ulster, while enjoying more possession, were having a tougher time in trying to break down their opponent's defence. When they eventually did cross from a driving maul, Marmion managed to hold up McBurney.
With hooker Rob Herring picking up an injury during the warm-up and regular line-out caller Iain Henderson out of action, Ulster's set-piece malfunctioned and late in the opening half they threw away the opportunity to reduce the deficit with an overthrown line-out on Connacht's five-metre line.
Ulster improve to set up tense finish
It was a flat opening 40 minutes from Ulster, whose semi-final place was assured on Saturday when Glasgow fell to defeat by Edinburgh.
They did improve after the break, with half-back pair Alby Mathewson and Ian Madigan coming on to make their debuts for the province.
Marmion once again managed to hold McBurney up over the line as Ulster's ball-carriers began to assert their authority, and their breakthrough came on 49 minutes when Billy Burns' pass put Stockdale in.
Despite spending less time in opposition territory, Connacht continued to look dangerous with the ball and thought they had extended their lead through Tom Farrell, only for the centre to knock the ball on while grounding.
Farrell's midfield partner Aki, celebrating his 100th Connacht cap, had no such issues a minute later when he received the ball eight metres out and crashed through three defenders to ground, capping a fine individual performance.
Ulster ensured the game would go down to the wire as Timoney drove over from the back of the scrum, but it was Connacht who had the final say as replacement Aungier added the bonus point in the last minute to secure the win.
Ulster: Stockdale; Gilroy, Hume, McCloskey, Ludik; Burns (c), Cooney; McGrath, McBurney, Moore, A O'Connor, Treadwell; Timoney, Murphy, Coetzee.
Replacements: Andrew, O'Sullivan, O'Toole, Carter, Rea, Mathewson, Madigan, Lowry.
Connacht: Porch; Sullivan, Aki, T Farrell, Wootton; Carty, Marmion; Buckley, Heffernan, Bealham, Dillane, Thornbury; Masterson, Butler, Boyle.
Replacements: Murphy, Duggan, Aungier, Murray, Oliver, Kerins, Dean, Daly.