Simmons notched 102 off 84 balls to help the Windies recover from a precarious position of 87-5 after 24 overs.
Kevin O'Brien claimed the first wicket of the day when Dwayne Smith lofted a catch to John Mooney at mid-on. Darren Bravo followed Smith straight back to the pavilion soon after when he was run out by Andy McBrine.
West Indies opener Chris Gayle scored 36 before he was caught by O'Brien off the bowling of George Dockrell. The Irish bowler then struck again just two balls later when he trapped Marlon Samuels lbw for 21.
Dockrell claimed his third wicket of the innings in the same fashion as his delivery struck Denesh Ramdin's pad and, with the Windies out of reviews, he was dismissed for one.
Simmons joined Darren Sammy at the crease and they led the West Indies recovery with some composed stroke play. The pair put on a partnership of 154 before Sammy was caught out on 89 by Dockrell off the bowling of Rooney.
Simmons brought up his century with two balls of the innings remaining courtesy of a boundary, before sending a catch to Dockrell on the next ball to bring his knock to an end.