CHICAGO -- Believe it or not, the White Sox did not do any scoreboard watching during a 4-2 victory over the Rockies Tuesday night at Guaranteed Rate Field.

Or at least that’s the company line collectively espoused after raising their record to 10-4 with Miguel Cairo serving as acting manager.

“No. I don't pay attention to that,” said White Sox designated hitter Eloy Jiménez, whose three-run home run helped end the team’s four-game Interleague losing streak. “They need to do their thing and we need to do our thing."

“I don’t really care what they do. We’ve got to take care of business,” Cairo said. “We play the way we’re supposed to play, anything can happen.”

For those who didn’t check the final scores, Cleveland claimed a 3-1 victory over the Angels to maintain a three-game lead over the White Sox (73-69) in the American League Central and reduce their elimination number to 19. The two play a makeup game Thursday afternoon at Progressive Field before Cleveland comes to Chicago for three night games from Sept. 20-22.

But let’s go with the assumption Chicago isn’t overly focused on the Guardians right now, if giving them any focus at all. With 20 games left to play, the White Sox have to like what they see from their group.

José Abreu went deep for the first time since Aug. 3 against Kansas City, covering a career-high 37-game homerless stretch and 162 plate appearances. It’s not as if Abreu is struggling at the plate, with his .312 batting average ranking third in the AL behind Luis Arraez (.319) and Xander Bogaerts (.318).

There’s just been a lack of consistent power for the first baseman sitting third all time in franchise history with 243 homers.

“He’s been getting good at-bats. He’s taking his walks and he’s getting on base,” Cairo said of Abreu, who has a .386 on-base percentage. “Eloy behind him has been hitting homers. It’s a good combination. And today it was nice to see him go deep.”

The three-run blast for Jiménez off Chad Kuhl in the first inning followed Elvis Andrus’ double and an Abreu walk. He is slashing .500/.516/1.000 with two doubles, four home runs, 12 RBIs and seven runs scored over his last seven games, and doing it as the team’s designated hitter.

That’s the same designated hitter role Jiménez wanted absolutely no part of a few years ago. He has moved to that spot from left field to protect his legs after a hamstring injury. But while accepting the change, Jiménez still is not a fan.

“I need to do my job. It is what it is right now,” Jiménez said. “I just feel good because if I swing at strikes, it's going to be better. I know I have power to just hit on the barrel and the ball is going to be out. I just try to be a hitter first and then become a power hitter."

These power outputs made a winner of Michael Kopech (5-9), who allowed two runs over five innings with three strikeouts and no walks. Four relievers allowed two hits over four scoreless innings to keep pace with Cleveland.

Then again, Cleveland doesn’t matter at this point to the White Sox, and to be honest, that attitude makes sense. Chicago has fought back during the medical absence of manager Tony La Russa by focusing on one game at a time, so even with the season winding down, why change what has been working?

“Do I have a figure in my head of games we need to win to win this division? Sure,” White Sox general manager Rick Hahn said during a pregame Zoom. “But the reality is we’re only playing tonight’s game. You want to see that same level of energy and focus and competitiveness you’ve seen over the next few weeks. If we’re able to bring that every day over the next [20], we’re going to finish strong and make this thing interesting in the next month and into October.”

“It’s come down to the wire. We wouldn’t like it to be that way, but with all that’s happened for us this year, I think that us playing hard here towards the end has gone a long way,” Kopech said. “If we can keep scrapping it out and making sure these few weeks for us are important and competitive, then I think we can do what everybody expects out of us.”