Soriano established a career high in runs batted in for the second straight night, having driven in six on Tuesday while the Yankees were overwhelming the Angels 14-7.
He had a grand slam and a solo homer on Wednesday after hitting two out of the park on Tuesday. In addition, he reached 2,000 hits for his career last Saturday.
The Yankees scored four times in both the first and second innings on their way to a fourth straight win as they try to battle their way back into the playoff race. They began the night 5 1/2 games out of the American League's second wild card spot.
He then had a two-run double during the second and hit a solo home run in the fifth, giving him 24 for the season.
New York had 12 hits to make things easy for Ivan Nova (6-4), who allowed three runs on 10 hits in 7 1/3 innings.
The Yankees roughed up Jared Weaver (7-6) for nine runs and nine hits in five frames.
Alex Rodriguez went 1-for-4 and scored twice as he plays while appealing a 211-game suspension. He has a .258 batting average in eight games this season.