Diamond (6-11) was spotted to a 4-0 lead in the second inning and made it stand. He retired the first eight batters of the game and allowed just three hits -- including a home run by Alejandro De Aza -- through the first six innings.
The White Sox scored twice in the seventh, with Jordan Danks delivering a two-run single. Casey Fien came in for Diamond and struck out Josh Phegley.
Glen Perkins struck out two of the three batters he faced in the ninth in getting is 36th save.
The Twins reached Chicago starter John Danks (4-14) for seven hits and four runs in the first two innings. After that John Danks retired 16 straight, with 11 coming on ground ball outs.
Minnesota built its 4-0 lead with Oswaldo Arcia singling in Alex Presley with two out in the first and Chris Colabello knocking a run in the second ahead of a two-run single by Eric Fryer.