The right-hander coasted through eight scoreless innings, allowing four hits, a walk and striking out nine. Hernandez (4-0) has gone consecutive starts without allowing a run.
"They gave me four runs in the second inning and I said, 'That's enough. No more runs,'" a smiling Hernandez said.
In his last start against Tampa Bay he pitched seven innings in a 1-0 win. He extended his streak to 19 scoreless innings against the White Sox.
In the opener, Bartolo Colon pitched seven strong innings and Paul Konerko hit a two-run double to lead Chicago to a 2-1 victory. At 1 hour, 52 minutes, it was the fastest game in the majors this season, according to the Elias Sports Bureau.
The White Sox won despite having as many hits (two) as errors.
"That's a miracle," Chicago manager Ozzie Guillen said.
Betancourt matched a career high with four hits in the second game, including a three-run homer. Branyan finished 5 of 5 for the Mariners, who compiled a season-high 19 hits.
"I've never been given a shot to really play this game on an everyday basis," Branyan said. "What is happening this year is a first go around for me."
Chicago starter John Danks (2-1) yielded five runs and eight hits in four innings.
"Obviously I didn't expect to go four and give up five runs," Danks said. "I felt I had plenty of stuff to give us chance to win and I knew I was up against Felix and he is one of the best in the game right now. Anytime you give up five runs you can pretty much pack it in. He's that good and I put us in a hole I couldn't get out of and I take full blame for that."
In the opener, Mariners starter Chris Jakubauskas (1-3) was a hard-luck loser in his first career complete game. The White Sox were held to seven hits in the doubleheader.
With one out in the second, Danks allowed consecutive singles before Betancourt homered on a 2-2 pitch, his first of the season.
Betancourt added RBI singles in the fourth and seventh. Branyan had an RBI single in eighth.
Colon (2-1) bounced back after struggling in his previous start at Baltimore. The burly right-hander allowed an unearned run and four hits, pitching out of a jam in the seventh. He struck out six and walked one.
Bobby Jenks pitched around third baseman Josh Fields' error in the ninth for his fourth save. With runners on first and second, he struck out pinch-hitter Sweeney swinging and got pinch-hitter Wladimir Balentien on a fly to center.
The game was a makeup of Monday night's rainout.
Jakubauskas, making his third start in place of injured Ryan Rowland-Smith, retired his first 10 batters. He walked Fields in the fourth, then allowed a single to Carlos Quentin. With two outs, Konerko doubled down the left-field line.
"One negative. The ball I left out over the plate to Konerko and he hit it down the line," Jakubauskas said. "It's just one of those things. I missed my spot and it came back to bite us."
Ken Griffey Jr. returned to Chicago after playing 41 games for the White Sox last season and had a double in the opener. ... DH Jim Thome (heel) didn't play in either game. Guillen hopes to have him back when the White Sox open a three-game series in Texas on Friday. ... 2B Chris Getz (broken middle finger on his right hand) took some batting practice before the game and said it went fine. Getz said the swelling had gone down and he hopes to play Wednesday. He has missed four consecutive games. ... Mariners C Kenji Johjima, on the 15-day DL with a strained right hamstring, could return May 1 when he's eligible.