Ibanez smacked an 0-1 pitch from closer Esteban Yan (5-7) off the foul pole in right field. The first baseman also knotted the contest at 4-4 in the seventh with a sacrifice fly, helping to increase his career highs to 19 home runs and 80 RBI.
Joe Randa recorded his 500th career RBI with a sacrifice fly in the fourth for the Royals, who beat the Devil Rays for the third time in four meetings this season.
Rookie reliever Ryan Bukvich (1-0) struck out two in a scoreless eighth to pick up his first major league win.
Tampa Bay rookie Carl Crawford had a solo shot and a season-high three RBI and Jared Sandberg drove home two runs. But the Devil Rays slipped to 1-3 on their current six-game homestand.