Santana (7-3) gave up five hits and a season-high four walks in 6 2/3 innings. The major leagues' strikeout leader had just three, none after the second inning.
Upset after Blum's at-bat, Santana gave up Jackson's double. He then approached Kelley to find out where the pitches to Blum were.
"He told me the first pitch was out of the strike zone," Santana said. "I asked him what about the others, and I didn't get an answer. I think if you're an umpire you should know what you're doing and I think you've got to have an answer."
Santana argued with Kelley before being restrained by catcher Mike Redmond. Manager Ron Gardenhire came out to remove Santana and then was ejected by Kelley when he shouted in the umpire's direction.
"The man behind the plate had a bad inning," Gardenhire said. "Everything that was a strike became a ball. It's too bad when the game gets away from you like that. Johan deserves a lot more respect than that."
The umpires, through a clubhouse attendant, refused to comment after the game.
"I thought he was fair," May said of Kelley. "You can't argue balls and strikes and you're not going to win that battle so it doesn't matter."
Santana hasn't won at the Metrodome since April 10. He lost to a National League team for the first time since June 10, 2002, against Atlanta, falling to 11-2 in interleague play.
May (1-1), who started in place of Jake Peavy so the Padres ace could face division rival Los Angeles on Monday, gave up just three hits in six innings. Matthew LeCroy's homer in the fifth was his only mistake.
The Twins managed only four hits in losing for the fourth time in six games. May, in just his third start of the season, didn't walk anyone and struck out four despite pitching on only three days' rest following a 5 2/3 inning relief appearance against Detroit on Wednesday.
"The three days' rest for me is a good thing," May said. "It gave me time to think between outings and carry the momentum from my last outing."
The Padres won their second straight following a five-game losing streak and won their first series since taking two of three from Milwaukee on May 30-June 1. They are just 5-12 in June after going 22-6 in May.
"We played well and we had to beat Santana," manager Bruce Bochy said.
LeCroy led off the Twins' fifth with a solo homer, his sixth of the season. Dave Roberts matched that run with a solo shot of his own in the top of the sixth. Roberts' fourth homer of the season marked a career high.
The Padres have won all three of May's starts this year. ... Minnesota rookie Glenn Williams has hit safely in all seven games with the team. ... Luis Rivas made his first career start at shortstop for the Twins in his fifth full season with the team. He and brought the crowd to its feet in the second inning when he made a diving stop of Ojeda's grounder and threw the Padres catcher out at first. Rivas had appeared as a defensive replacement at shortstop three times.