Mike Sweeney homered and drove in five runs as the Royals took an 8-0 lead after six.
The Twins scored two in the seventh, three in the eighth and then three in the ninth against closer Mike MacDougal to tie the game. But Kansas City answered in the bottom half.
Eddie Guardado (0-2) walked Beltran leading off the ninth, then his wild pitch put Beltran on second before Ibanez singled into right. Beltran barely slid safely under the tag after a strong throw from Dustan Mohr.
MacDougal (3-3) got the win despite allowing three runs and four hits in the ninth.
Darrell May, looking for his first win in 15 starts, left with an 8-1 lead and the bases loaded in the seventh, then an RBI groundout made it 8-2 but the bullpen blew it.
May is 0-4 with 11 no-decisions in 15 starts since beating the Chicago White Sox last Sept. 11.
Sweeney, whose two-run single in the bottom of the ninth beat San Francisco on Sunday, is hitting .381 with three home runs and 16 RBI during an 11-game hitting streak.
It was the sixth time he'd matched his career high with five RBI and the first time he'd done it since last June 20 against San Diego.
May went 6 1/3 innings, giving up two runs on seven hits. May walked two and struck out four and left after A.J. Pierzynski's bases-loaded single scored a run in the seventh.
Lohse, whose 2.91 ERA coming into the game was second best in the league, gave up five runs and eight hits in five innings.
Beltran had two hits for the Royals, including an RBI double, giving him six multihit games this month.
Aaron Guiel's RBI single put the Royals ahead 2-0 in the fourth, then Michael Tucker and Joe Randa singled in the fifth before Sweeney drove Lohse's first pitch 431 feet into the water display behind left field.
Randa had an RBI groundout in the sixth.
The game was the makeup of one rained out April 23. ... RHP Mike Fetters tried to go through a throwing routine in the bullpen Monday but had to stop when his pitching elbow started swelling up. The Twins planned to get a second opinion from a specialist before deciding what to do. ... RHP Albie Lopez was activated from the 15-day DL, and LHP Les Walrond was sent to Triple-A Omaha, leaving the Royals without a left-handed reliever. ... Lohse's ERA climbed from 2.91 to 3.23.