From an ESPN article and MLB article about a game between the Dodgers and Angels played in 2008:
The final score was 1-0, marking the fifth time since 1900 that a team
did not get a hit but won the game.
Complete List:
Cnt Date Tm Opp GmReslt PA AB R H 2B 3B HR RBI BB IBB SO HBP SH SF ROE GDP SB CS LOB Batrs
+----+-------------+---+----+-------+---+---+--+--+--+--+--+---+--+---+--+---+--+--+---+---+--+--+---+-----+
1 1992-04-12(1) CLE BOS W 2-1 32 25 2 0 0 0 0 2 7 0 6 0 0 0 1 0 6 1 6 9
2 1990-07-01 CHW NYY W 4-0 31 26 4 0 0 0 0 0 5 0 3 0 0 0 3 0 1 1 3 11
3 1967-04-30(1) DET @BAL W 2-1 40 24 2 0 0 0 0 0 10 1 3 2 4 0 1 1 1 0 11 14
4 1964-04-23 CIN @HOU W 1-0 31 29 1 0 0 0 0 0 2 0 9 0 0 0 2 0 0 0 3 10
5 2008-06-28 LAD LAA W 1-0 29 24 1 0 0 0 0 1 3 0 9 1 0 1 1 0 1 0 4 13
Source: Baseball Reference (Included code is of respective website.)
Wikipedia article on these win:
five times a team has been no-hit and still won the game: two notable victories occurred when the Cincinnati Reds defeated the Houston Colt .45s (now called the Houston Astros) 1–0 on April 23, 1964 even though they were no-hit by Houston starter Ken Johnson, and the Detroit Tigers defeated the Baltimore Orioles 2–1 on April 30, 1967 even though they were no-hit by Baltimore starter Steve Barber and reliever Stu Miller.
Another list that may be helpful from Baseball Reference.