Kansas City scored three runs in the top of the 11th to put the game away after giving up three earlier leads.
In the top of the 11th, Velazquez plated automatic runner Freddy Fermin with a double to centre, then scored on Adam Frazier's infield single. Maikel Garcia added on with an RBI single.
The Royals had gone ahead 4-3 in the top of the 10th on Vinnie Pasquantino's sacrifice fly to left, but the Rays tied it for a third time in the bottom of the inning when Jonny DeLuca doubled to left to score Harold Ramirez.
James McArthur (2-2) got the win with two innings of relief, and Nick Anderson picked up his first save. Former Royals left-hander Richard Lovelady (0-3) took the loss.
Orioles 5 White Sox 3
Ryan O'Hearn, Anthony Santander and Jordan Westburg homered in the eighth inning as Baltimore rallied for a victory against host Chicago.
The three-homer barrage across a five-batter stretch created a stunning turnaround after the Orioles had only three singles entering the eighth. Baltimore starter Albert Suarez pitched four shutout innings in his longest outing since April.
White Sox starter Erick Fedde pitched 6 1/3 shutout innings and Gavin Sheets smacked a two-out, bases-loaded triple in the fifth inning for the team's only runs. Chicago lost for the eighth time in nine games.
Giants 7 Mets 2 (10 innings)
Brett Wisely had three hits, including a tiebreaking RBI single leading off the 10th inning, as visiting San Francisco mounted another late-inning comeback to defeat New York in the middle game of a three-game series.
Patrick Bailey had an RBI single in the sixth and LaMonte Wade Jr. tied the score with a run-scoring single in the ninth for the Giants, who have won four straight, all after trailing in the eighth inning or later.
After Wisely's 10th-inning single against Sean Reid-Foley (1-2), Bailey ended up walking with the bases loaded and Mike Yastrzemski laced a three-run triple two outs later. Starling Marte belted his sixth homer of the season in the second and Brett Baty hit a tiebreaking solo shot in the seventh to account for the Mets' runs.
Tigers 2 Blue Jays 1
Kerry Carpenter hit a two-run homer, Reese Olson recorded his first win this season in his 10th start and host Detroit topped Toronto.
Olson (1-5) was forced to leave his previous start at Kansas City with a right hip contusion after being struck by a line drive. He limited the Blue Jays to one unearned run and three hits in 6 1/3 innings. Tyler Holton pitched the ninth for his first save this year and the second of his career.
Blue Jays starter Jose Berrios (5-4) allowed two runs and seven hits while striking out five in seven innings. Davis Schneider drove in Toronto's lone run with a double.
Twins 5 Rangers 3
Alex Kirilloff blasted a three-run homer in the bottom of the eighth inning to help Minnesota rally for a win against Texas in the second game of a three-game series in Minneapolis.
Twins starter Chris Paddack allowed two runs and four hits in five innings. Cole Sands (2-0) threw two innings of scoreless relief before Jhoan Duran pitched the ninth to earn his sixth save for Minnesota, which has won four in a row following a seven-game losing streak.
Rangers starter Michael Lorenzen allowed one run and three hits over six innings. Ezequiel Duran homered and Leody Taveras had two hits and an RBI for Texas, which has lost six in a row and 12 of its past 14.
