Trailing 3-2, the Devil Rays loaded the bases with no outs against Luke Hudson (0-1) in the seventh. Andrew Sisco came in to strike out Travis Lee before Jonny Gomes walked on four pitches to tie the game. After pinch-hitter Damon Hollins struck out, Wigginton lined a two-run single to center to give the Devil Rays a 5-3 lead.
Tampa Bay added a run in the eighth on Carl Crawford's RBI double to make it 6-3.
Shawn Camp pitched two innings for his first save.
Kansas City took a 3-2 lead in the top of the seventh on Mark Grudzielanek's sacrifice fly off Seth McClung (1-2).
McClung gave up three runs and nine hits in seven innings. He had allowed 12 runs and 12 hits over eight innings in losing his previous two starts of the season.
Royals right-hander Mike Wood gave up two runs and three hits in four-plus innings. He struck out four and walked five.
Kansas City, which has lost six straight, is still looking for its first win this season from a starting pitcher. The starters have failed to pitch into the sixth inning in six of 10 games and are 0-6.
The Devil Rays took a 1-0 lead on a second-inning RBI groundout by Wigginton.
Kansas City loaded the bases -- on an infield single and two walks -- with two outs in the third, but failed to score when Reggie Sanders' lined out.
The Devil Rays made it 2-0 when Crawford scored from third on Russell Branyan's sacrifice fly.
Angel Berroa got Kansas City within 2-1 on a run-scoring infield single in the fourth. Mark Teahen's sacrifice fly in the sixth tied it at 2-all.
Royals CF David DeJesus (left hamstring) was in the lineup after missing the past six games. He was 1-for-3 with a walk. ... Devil Rays SS Tomas Perez landed on the ground behind the Royals' bullpen bench after he just missed catching DeJesus' foul ball in the fifth. He remained in the game.