The White Sox went ahead to stay with three unearned runs off Robbie Ross (1-1) in the fifth, including Abreu's fifth homer of the season for a 5-2 lead.
Johnson (1-1) allowed two runs and only a single over his five innings, but the right-hander walked the leadoff batter the first four innings and threw only 44 of his 87 pitches for strikes. The Rangers also scored on a wild pitch, and had another runner thrown out trying to do the same.
Ronald Belisario threw two scoreless innings before Andre Rienzo and Matt Lindstrom each worked an inning.