Abreu was hitless in his three previous at-bats, continuously jammed with the inside fastball. Gregerson took the same approach, but left his second pitch up and watched it quickly leave the park.
"I was trying to pound him in, pound him in," said Gregerson. "I thought I threw some pretty good pitches. The first one, he swung over the top in the dirt. The second one, sinker down and in. I think it caught the corner. He just opened up quick and was right on top of it."
The inning began with Fernando Abad on the mound. The lefty struck out Alejandro De Aza before offering up back-to-back singles to Gordon Beckham and Conor Gillaspie and departing in favor of Gregerson.
It was Abad who was charged with the loss, his first of the season but the A's bullpen's American League-leading eighth -- representing half of the club's losses.
The A's had just six losses when leading after the seventh inning last season. Through 41 games, they have five.
"Certain parts of the team are going to struggle at times," said Tommy Milone, who worked six impressive innings. "It just happens, it's part of the game and it's just something we have to deal with."
Sean Doolittle would've pitched the ninth, manager Bob Melvin said, had a save situation remained intact. Instead, it went to Gregerson, who wasn't that unhappy with his pitch to Abreu.
"He's a good hitter," he said. "He's obviously shown that his first month and a half of the season or so. You try to throw him pitches that aren't around the strike zone. You try to make him fish, which he definitely does.
"I don't think it was really a bad pitch. It was just something he was ready for. He was looking for it. We've been doing it to him the whole series, pound him in. It just stayed up a little too much. Any other day it could be a ground out to third base, we get a double play."
As a result, Milone settled for a no-decision despite putting together yet another impressive outing to go along with a pair of homers from John Jaso and Josh Donaldson -- two of just three A's hits.
Milone gave the A's six innings of one-run ball, his only mistake coming on his first pitch of the game -- a fastball to Beckham that he clubbed for a home run.
Jaso did his best Beckham impression in the bottom of the inning, driving Andre Rienzo's third pitch over the right-field wall for his third homer in his last four games. It was the first time the A's had played a game in which both teams hit a leadoff home run since Aug. 30, 2002.
Donaldson's shot -- his ninth of the year and the A's 13th in the last seven games -- led off the fourth against Rienzo, who gave the White Sox 6 1/3 innings.
Outside of the home run, Milone scattered just four other hits and didn't walk a batter. The southpaw struck out four and has allowed just one earned run over his last 14 innings, after surrendering 10 in his previous 10 2/3 innings.
"Fastball inside. I was really able to locate it, and go upstairs when I needed to," Milone said of his success Wednesday. "Just trying to keep them off balance and not so predictable. I know teams know me by now. They know I throw the changeup a lot, so I'm trying to use my fastball as much as possible.
"I'm trying to get back to being consistent. The last two starts I've been able to do that."
A's starters have a 1.17 ERA during their past seven games, having offered up just six runs in a combined 46 innings. They have a 2.97 ERA on the season, which ranks second in the league only to Detroit's 2.79 mark.
A 6-4 homestand behind them, the A's will hit the road for their third straight three-city road trip, hitting Cleveland, St. Petersburg and Toronto for a nine-game swing.
"We got off to a little bit of a slow start on the homestand, but came back and played really well," said Melvin. "We're in a position to potentially win the game today. It just ends up being a pitch to a guy who hit a three-run homer. Seems like he's hit a few of those."