White Sox complete sweep of Giants with 13-4 rout; Twins next

SAN FRANCISCO — The White Sox completed a three-game sweep of the Giants and a 4-2 road trip Sunday.

Monday being the Fourth of July, there’s no better time for a team that considers itself postseason material to get hot.

The Sox are 38-39 and in need of a hot streak. And they finally are showing signs of maybe, just maybe, turning the corner and having the wherewithal to go on one.

‘‘We came to play this series,’’ said right-hander Lucas Giolito, who allowed one run in six innings in the Sox’ 13-4 rout Sunday. ‘‘This is the brand of baseball the Chicago White Sox are all about. It’s been a rough year, to say the least, dealing with injuries and some tough series and losing streaks. This series, we were able to put our foot on the gas.’’

Now they have to keep it there, right-hander Lance Lynn said.

‘‘You’ve seen us get back to or close to .500, and we’ll go back to four under,’’ said Lynn, whose six scoreless innings Friday set the tone for the sweep. ‘‘We have to fight to get back to .500 and, when we get there, don’t let up. It can’t be, ‘Push to get there,’ then when we get there, ‘OK.’ Can’t take a deep breath and see what’s going on. There’s no more deep breaths. We have to keep going and keep pushing till the end of the year.’’

Now is the time for a push, with the American League Central-leading Twins in town for three games. They lead the Sox, the team that was supposed to be leading them by now, by 4½ games. Between now and the All-Star break in two weeks, the Sox have 15 games in 14 days against AL Central teams.

It’s an important stretch.

‘‘Big time,’’ said outfielder Adam Engel, who will bolster the Sox’ depth when he comes off the injured list any day now. ‘‘Division games are big. When this team is playing good baseball, it doesn’t matter who we’re playing, we have a good chance to win. We just have to keep playing good ball.’’

Giolito picked up where Lynn and right-hander Dylan Cease (one run in five innings Saturday) left off, striking out seven in his first three innings, then pitching to contact in his last three.

Featuring what he called his best changeup of the season, he gave up three hits and walked two in his second consecutive good start after four or five bad ones, an encouraging sign for the Sox. Diving, running catches in the outfield by infielders Josh Harrison and Yoan Moncada helped.

‘‘We have to get busy before the All-Star break,’’ Harrison said. ‘‘[The Twins] are our next opponent, so they’re the most important. Whoever is after them is the most important. We took care of the Giants this weekend, and with the Twins coming in, we have to take care of them.’’

A victory Monday would put the Sox at .500 for the first time since June 21. They followed that by losing four in a row.

‘‘Can’t get over [.500] till you get there,’’ manager Tony La Russa said. ‘‘We get [closer] Liam [Hendriks] back [Monday], and the club is more complete than it’s been. Two weeks in the Central. That will be fun, head-to-head. The Twins are for real and Cleveland is for real. It’s exactly what you need, man. You need to play against tough competition; that’s how you get better.’’

Luis Robert singled in two runs in the third to get the Sox’ offense going, and Gavin Sheets drove in three runs with his third double in two days in the fifth. In a five-run eighth, Seby Zavala doubled in a run and Andrew Vaughn singled home a pair. The Sox had 17 hits, three each by Zavala and Leury Garcia.

‘‘We played six games on the road trip as hard as we could,’’ La Russa said. ‘‘We were really ready to play all six times. The effort shows you how special these guys are.’’