Ian Keatley, who has signed for Munster, kicked two penalties in his final appearance for a spirited but well-beaten Connacht side.
Having gotten over their disappointing European exit, Munster will host last season's champions the Ospreys in a heavyweight semi-final clash at Thomond Park next Saturday.
Their opening try came out of nothing. Johne Murphy fired a hopeful kick skyward and Gavin Duffy looked certain to claim it, but Zebo was quickly in to rob him and sprint over unopposed in the left corner.
A great catch by Duffy helped set up an immediate opportunity for Keatley to reply. However, the out-half's penalty attempt bounced off the right hand post and away in a blustery wind.
Munster's forwards, with fit-again captain Paul O'Connell back at the helm, exerted control in the maul and in the loose. However, Connacht were doughty in defence and kept their discipline in a well-contested first half.
Keatley opened their account in the 30th minute, punishing Quinlan for slowing up Connacht ball, and he kicked the visitors in front six minutes later.
But Munster got back on top before the break, launching a penalty to touch before a well-constructed drive ended with Quinlan crashing over to the left of the posts. Ronan O'Gara added the conversion for a 12-6 interval lead.
Tony McGahan's men made a smart start to the second half, O'Gara tucking away a penalty as the home forwards gained ground once again.
Keatley miscued a 53rd minute penalty and Connacht full-back Duffy had a try disallowed for an earlier indiscretion by Johnny O'Connor which was spotted by assistant referee John Carvill.
Sean Cronin, who scored a terrific try recently against Ulster, took a brilliant line to almost unlock Munster out wide on the right. But the westerners could not break down Munster's well-organised defence.
A late surge from the home side yielded a try for Howlett, who did well to dive on a kick through from Warwick before the ball bounced over the end-line.
O'Gara knocked over the conversion for good measure and not even a last-minute yellow card for O'Connell, who went offside at a ruck, could spoil a satisfying night for Munster.
Giving his reaction afterwards, Munster head coach McGahan said: "There may potentially be two games remaining and selections will have to be looked at as we move on.
"We have the Ospreys next up and we certainly know each other very well. There is always just a score between us so of course we face a difficult task back here next week."
|Munster Rugby Score Card|
|Connacht Rugby Score Card|