Has any Major League Baseball team won a game with out a hit?

Answer 1

Yes, that has happened thrice.

The Cincinnati Reds defeated the Houston Colt .45s on April 23, 1964 by the score of 1-0 without getting a hit. Pitcher Ken Johnson of the Colt .45s is the only pitcher in MLB history to throw a 9 inning no hitter and lose the game. The Reds run scored on an error, ground out advancing the runner, and a second error.

Steve Barber and Stu Miller of the Baltimore Orioles combined on a no hitter of the Detroit Tigers on April 30, 1967 but lost the game 2-1. The Tigers scored two runs in the 9th inning on a walk, another walk, a sacrifice moving the runners to 2nd and 3rd, wild pitch scoring the first runner and advancing the second runner to 3rd, another walk, and a fielder's choice which scored the second run.

Andy Hawkins, pitching for the New York Yankees and facing the Chicago White Sox at Comiskey Park on July 1, 1990, was saddled with a 4-0 loss and did not surrender a hit. On that day, Hawkins pitched well throughout the game, but sloppy defense let him down. With 2 outs in the 8th, Sammy Sosa reached base after an error by Yankee 3rd baseman Mike Blowers. Hawkins then walked the next 2 hitters. Robin Ventura then hit a flyball to left field. Rookie Jim Leyritz was in left, although he was normally an infielder. The Chicago winds didn't help either, and Leyritz muffed the catch, which allowed all 3 runners to come home. Ivan Calderon hit a flyball to right, and rightfielder Jesse Barfield lost it in the sun, and again a flyball was dropped that allowed Ventura to score. When the inning was finally over, the Yankees committed 3 errors, 2 walks and 4 unearned runs.