Calvin Nash sent out a timely reminder to Johann van Graan as he ran in two tries in an entertaining clash at the Sportsground where both sides surrendered 12-point leads.
Nash, with just six first appearances this season and with Munster set to rotate in their remaining PRO14 games against Scarlets and Benetton, also spent a spell in the bin for a deliberate knock-on in the opening half.
Hooker Dylan Tierney-Martin and winger Diarmuid Kilgallen scored tries for Connacht who lead 12-0 after 22 minutes but Munster took over and tries from Nash and Liam Coombes, along with the boot of Jake Flannery helped them lead 17-12 at the break. Quick-thinking from Jack Crowley set up Nash for his second try with a crossfield kick as they went 24-12 in front but Connacht fought back. A try from replacement scrum-half Stephen Kerins got them back in contention and former Galway All-Ireland minor hurling winner Shane Jennings levelled with a try in the left corner but Conor Fitzgerald missed the difficult conversion.