Severino (5-3, 2.77) allowed five hits and struck out two as the Yankees reduced their magic number for clinching an AL wild card spot to three.
The Yankees took advantage of three White Sox errors and Dustin Ackley homered for the Yankees in a two-run sixth.
Jacoby Ellsbury took advantage of two errors by White Sox first baseman Jose Abreu to score in the first and Slade Heathcott scored on a passed ball in the sixth after Ackley's homer.
Heathcott drove in a run on a sac fly in the eighth after the White Sox's third error and and Ellsbury had an RBI single. Greg Bird had an RBI double and scored twice.
Justin Wilson gave up a homer to pinch hitter Avisail Garcia the seventh. Dellin Betances pitched the eighth and Bryan Mitchell ninth as the Yankees improved to a major league-best 65-2 when leading after six innings.
The Yankees host Boston in a four-game series starting Monday (7:05 p.m.) Ivan Nova (6-9, 4.87) faces Eduardo Rodriguez (9-6, 3.97).