Hurricane Frances caused the Devil Rays to arrive three hours after the scheduled start.
The postponed game will be made up today as part of a doubleheader, beginning at 4:05pm.
Lieber (11-8) allowed nine hits and walked none in 6 2-3 innings.
Jorge Sosa (3-4) gave up five runs and nine hits in four-plus innings.
Twins 3, Orioles 1
In Baltimore, Mike Cuddyer snapped a tie with a two-run homer in the ninth inning, and Minnesota rallied to beat the Orioles.
The Twins pulled even with an eighth-inning run, then took control in the ninth against Jorge Julio (2-4). Pinch-hitter Jason Kubel drew a one-out walk, and after Cristian Guzman hit a fly ball, Cuddyer drove a 1-0 pitch deep into the left-field seats.
It was his ninth home run, the first since July 31.
Julio then threw a high inside pitch that nearly hit Augie Ojeda in the head, and plate umpire Ron Kulpa promptly ejected the right-hander.
J.C. Romero (7-1) pitched a scoreless eighth for the Twins, extending his club-record run of shutout innings to 34. Joe Nathan worked the ninth for his 39th save.
Royals 6, Tigers 2
In Detroit, Dee Brown homered twice and drove in four runs to lead Kansas City over Detroit.
Jimmy Serrano (1-1) picked up his first major league victory with three scoreless innings of relief, helping the Royals win for just the fifth time in 16 games.
Carlos Pena and Craig Monroe homered for the Tigers.
Nate Robertson (12-8) allowed five runs and nine hits in six-plus innings, losing for the first time in four starts.
RSS