With more reminders of Adam Eaton trade coming, White Sox’ Lucas Giolito dominant again in victory vs. Indians

Right-hander Lucas Giolito won’t get the chance to face his old organization this week in Washington, but he offered another reminder Sunday of why the White Sox acquired him from the Nationals in an organization-changing move.

Giolito allowed five hits and struck out nine in 7⅓ scoreless innings in the Sox’ 2-0 victory against the Indians. He has won seven consecutive decisions — the most by a Sox pitcher since Chris Sale won nine in a row in 2016 — and has a 1.92 ERA with 66 strikeouts during the streak.

Perhaps most important, however, is that Giolito again controlled the strike zone. He walked 90 batters last season but none Sunday, the first time he has done that this season.

‘‘Limiting walks was one of my main goals going into this year, as far as stats and everything,’’ Giolito said. ‘‘Like I’ve been saying, it’s all about just attacking the zone, not being afraid of any hitter that steps in the box, going after him.’’

Giolito (8-1, 2.54 ERA) helped the Sox complete a 6-1 homestand and moved them back to one game below .500 at 29-30. He has a strong chance to be an All-Star and the American League pitcher of the month for May in a career that already has featured plenty of ups and downs.

But if Giolito is reflecting on everything that has happened to him before and since he left the Nationals, he isn’t saying.

‘‘Not too much; I’m here now,’’ Giolito said. ‘‘Been here for a few years. Just doing my best to help this team win ballgames.’’

That might be, but every time Giolito pitches the way he has recently, it’s a reminder of the Sox’ rebuild and what happened in December 2016.

The trade with the Nationals, which came a day after Sale was dealt to the Red Sox, brought back Giolito and fellow right-handers Reynaldo Lopez and Dane Dunning for outfielder Adam Eaton. Lopez will get the chance to start against his former team Tuesday, and he said the experience will be emotional because the Nationals were ‘‘the team that signed me and gave me the chance to play at this level.’’

Lopez recalled he wasn’t expecting to be traded when he was, but he knew what the move meant to the Sox’ franchise.

‘‘I knew the team was looking for young players to start their rebuilding process,’’ Lopez said through a translator. ‘‘Right now, I feel pretty proud to be part of this team and be part of the things we are building here.’’

Giolito was a major part of things Sunday, as was shortstop Tim Anderson.

Anderson gave the Sox the lead with his ninth homer of the season, a 429-foot drive against Indians starter Zach Plesac, in the fourth. His double against reliever A.J. Cole drove in Yolmer Sanchez and doubled the Sox’ lead in the eighth. It held up when Alex Colome picked up his 12th save.

‘‘Everybody’s been hoping to see the talent these guys have come to fruition,’’ manager Rick Renteria said. ‘‘They’re starting to scratch the surface. They should be excited. These are the real guys right now.’’

While Lopez has battled inconsistency this season and Dunning is recovering from Tommy John surgery, Giolito is emerging as an ace. He’s controlling his pitches, working quickly and looking nothing like the pitcher who struggled so much last season.

Anderson has an idea why.

‘‘A lot more focused and just believing in himself,’’ Anderson said. ‘‘He knows he’s dominant, so he goes out and proves it.’’