Conor Gillaspie had two hits and scored two runs for the White Sox, who rebounded from Friday's 8-7, 10-inning loss to the Mariners in the opener of this three-game set.
Chicago starter Dylan Axelrod earned a no-decision after giving up an unearned run on three hits over 5 2/3 innings.
Felix Hernandez (1-1) gave up four runs on six hits and two walks in 6 1/3 innings for Seattle, which has lost 12 of its last 14 games against the White Sox.
"The command was not there," Hernandez admitted.
A two-run homer by Michael Saunders off Chicago reliever Matt Thornton trimmed the Mariners' deficit to 4-3 with no outs in the eighth inning. Kendrys Morales hit a one-out single and Michael Morse followed with a walk against Jesse Crain, but Raul Ibanez struck out and Justin Smoak ended the inning with a 3-1 groundout.
Addison Reed recorded two strikeouts in a clean ninth inning for his third save of the season.
The Mariners got on the board in the second before the White Sox responded with four unanswered runs.
Ibanez stroked a one-out double, advanced to third base on a passed ball with two outs and scored on an E3.
Chicago tied things up in the fifth as Gillaspie led off the frame with his first career triple and scored on a sacrifice fly by Hector Gimenez.
"I got a couple pretty good pitches to hit and didn't miss them," Gillaspie said.
After White Sox reliever Donnie Veal (1-0) fanned Ibanez to escape a jam in the sixth, Rios took Hernandez deep with one out in the home half of the inning. The home run to left field plated Alejandro De Aza, who opened the frame with a single.
The White Sox loaded the bases with no outs against Hernandez in the seventh, but the damage was limited to just a De Aza sac fly.
Hernandez, who turns 27 on Monday, fell to 1-5 in eight career starts at U.S. Cellular Field ... The last five games between the White Sox and Mariners have been decided by one run ... Rios has now hit safely in 12 straight games against Seattle ... The Mariners haven't won consecutive games against the White Sox in Chicago since Aug. 11-12, 2007.
04/06 20:12:57 ET