The try-scoring continued four minutes after the restart when John Hodnett barrelled over, moments after Diarmuid Barron was held up just short of the line.
Connacht missed an opportunity to nudge back ahead when Iaone’s penalty struck the post, and Munster survived after the visitors won the ball back but some ferocious defence saw the ball held up over the line.
However, Munster were punished when David Hawkshaw scored the try of the match. Cathal Forde, Iaone and Dave Heffernan combined with some quick hands and Hawkshaw cut through the Munster defence to score unchallenged.
While Hawkshaw’s try was all about pace, Munster hit back through the power of Gavin Coombes.
The number eight collected the ball 10 metres out and used his strength to carry two Connacht players over the line with him, and Burns converted to put the hosts back in front.
Connacht refused to go away and the impressive Forde flew over in the 64th minute off the back of a scrum, and Iaone converted to put five between the sides once more.
Roared on by their home support, Munster had the final say with 10 minutes to play when Daly scored out wide, and 22-year-old Butler, on for the injured Burns, nailed the difficult conversion to secure an opening-day win.
While they fell to a defeat, Connacht have the consolation of taking two bonus points back to the Sportsground.
Munster: Mike Haley; Thaakir Abrahams, Tom Farrell, Alex Nankivell, Shane Daly; Billy Burns, Craig Casey; Jeremy Loughman, Diarmuid Barron (C), John Ryan; Jean Kleyn, Fineen Wycherley; Ruadhan Quinn, John Hodnett, Gavin Coombes.
Replacements: Niall Scannell, Josh Wycherley, Oli Jager, Alex Kendellen, Jack O’Donoghue, Ethan Coughlan, Tony Butler, Sean O’Brien.
Connacht: Santiago Cordero, Mack Hansen, Piers O’Conor, Cathal Forde, Shayne Bolton, Josh Ioane, Ben Murphy, Denis Buckley, Dave Heffernan, Jack Aungier, Joe Joyce, Darragh Murray, Josh Murphy, Conor Oliver, Cian Prendergast (C).
Replacements: Dylan Tierney-Martin, Peter Dooley, Sam Illo, Oisin Dowling, Shamus Hurley-Langton, Caolin Blade, David Hawkshaw, Sean Jansen.
