Connacht pushed Ulster all the way in their eventual 21-13 loss to Ulster at Kingspan Stadium on Saturday evening.
A 78th-minute try from Marcell Coetzee and Billy Burns’ conversion secured Ulster a May 17 date with Glasgow at Scotstoun in the penultimate stage of the Guinness PRO14 Final series.
Nick Timoney grabbing the northern province’s first try after 14 minutes in a tense knockout clash.
Ulster were ahead 11-3 at half-time after taking an early 8-0 lead and the hosts were never headed.
Ulster’s other points - on what was skipper Rory Best and replacement Darren Cave’s final game at the Kingspan - came from a conversion and two penalties from John Cooney.
Connacht, who trailed their hosts by just a point on two occasions, scored one try through Bundee Aki, with Jack Carty kicking a conversion and two penalties.
"In the end, there was always going to be a team disappointed and unfortunately, it was us," said Connacht head coach Andy Friend.