The 6-10 Johnson dunked on his own miss with 10:59 left to give the Seminoles a 47-45 lead - and they never looked back on their way to consecutive victories for the first time in a month, leading by as many as 16 at 72-56 with 2:53 left.
Johnson, who has had four double-doubles in the last five games, made 9 of 10 free throws, and the Seminoles connected of 19 of 21 tries at the line to go along with 48.9 percent shooting from the floor.
Florida State (15-6) used a 12-0 midway through the game to build a 38-31 lead, but UMass (10-11) countered with a 14-4 run of its own capped by James Life's 3-point shot that gave the Minutemen a 45-42 lead with 13:13 left.
Life, a transfer from Manatee Community College who played his prep ball at Mariner High School in Leigh Acres, led UMass with 14 points. Jeff Viggiano added 11, Brandon Thomas and Dante Mulligan 10 apiece for the Minutemen.
Al Thornton finished with 16 for Florida State and senior point guard Todd Galloway had 11.
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