On Monday night, it was Headley and the Yankees getting the upper hand on Garcia and the White Sox.
Headley has a .395 batting average and the Yankees take an eight-game winning streak into their Tuesday meeting with the White Sox.
Headley's average dropped 15 points after he went 1-for-4 with an RBI double in a 7-4 win that featured long home runs by Matt Holliday and Aaron Judge.
Despite the somewhat quiet night, the Yankees (9-4) would not be off to their best 13-game start going 10-3 in 2010 without their third baseman's production.
A year ago through New York's first 13 games, Headley posted a .182 average and the Yankees were 5-8.
After Monday, Headley has reached base in 12 games and reached more than once in nine games. He has been on base in 19 of his past 37 plate appearances, and he has a .509 on-base percentage.
"He's done it all, and it's a complete opposite of the way the year started last year, and it's great to see because we remember the struggles he went through last year," Yankees manager Joe Girardi said Monday afternoon.
Garcia went 1-for-4 and hit into two double plays Monday as his batting average dipped from .465 to .447. Garcia's quiet night was part of a mostly quiet night for Chicago, which has scored three runs or fewer in eight of 12 games.
White Sox third baseman Todd Frazier missed his second game recovering from the flu. Frazier, who is hitting .111 this season, could return Tuesday.
Chicago first baseman Jose Abreu was 0-for-4 and is 2-for-27 on the trip.
"I am struggling right now, but I'm trying to find a way to get out of it," Abreu said through an interpreter. "There are some at-bats where I can put the barrel on the ball, and there are some at-bats where I can find the ball in the strike zone. I am trying to figure out what's happening. I'm working on it."
New York's starting pitching has posted a 2.77 ERA during the eight-game streak after Jordan Montgomery allowed three runs and seven hits in six-plus innings Monday. Montgomery took a shutout into the seventh inning before Yolmer Sanchez hit a three-run homer.
The streak began when CC Sabathia pitched six innings in a come-from-behind 7-3 victory at Baltimore on April 9. In the eight-game run, the Yankees have 49 runs and 13 home runs.
"It's been exciting," Girardi said. "Our pitching has been tremendous. The starting pitching, it started last Sunday, eight days ago with CC. It's just continued with guys that have given us distance. The bullpen has done a tremendous job as it has all year and we've had some timely hitting and some big home runs."
On Tuesday, Luis Severino (1-0, 4.50 ERA) will get the ball, and the Yankees are curious to see if he can follow up his last start. On Thursday, Severino struck out a career-high 11, allowing five hits and two runs in seven innings during a 3-2 victory over the Tampa Bay Rays.
It was Severino's first win as a starting pitcher since beating the Chicago White Sox on Sept. 27, 2015.
Miguel Gonzalez (1-0, 4.22 ERA) makes his third start of the season for Chicago.
Gonzalez took a no-decision Thursday in Cleveland when he allowed three runs and eight hits in 4 2/3 innings. In his last 15 starts, Gonzalez is 5-5 with a 2.90 ERA.
Gonzalez is 4-4 with a 3.80 ERA in 14 starts against the Yankees, who are familiar with him from when the right-hander pitched for the Baltimore Orioles.