He still hasn't forgotten the snub, which made Saturday night's win particularly sweet.
Harrell pitched into the seventh inning and Jason Castro and Chris Carter homered in the fourth inning to give Houston the lead and the Astros held on for their third straight victory, 4-3 over the White Sox.
Harrell (5-7) allowed seven hits and three runs with a season-high seven strikeouts in 6 2/3 innings.
"It's always nice to beat them," said Harrell, who is 2-0 in two starts against the White Sox. "When someone tells you that you can't play for them and they don't think you're good enough there's a little chip on your shoulder when you play them."
The game was tied 1-1 when Castro launched a solo homer into the bullpen in right-center to start the fourth inning. Carter's one-out homer clanged off the foul pole in left field to extend the lead to 3-1 and leave starter John Danks (1-3) shaking his head. It was the team-leading 14th homer for Carter, who also leads the Astros with 36 RBIs.
He's the first Astro to have at least 14 home runs by June 15 since 2008.
Castro, the catcher, thought the fifth inning was important to help Harrell on the mound.
"That definitely took some pressure off Lucas and he was able to really focus on pitching," Castro said. "He's really good with that lead and maintaining it. Once we got that lead you could tell that he really kind of settled in and was ready to go deep into the game."
Brandon Barnes drove in a run with a double in the fifth inning to make it 4-1.
Danks yielded five hits and four runs in six-plus innings.
The White Sox had runners at the corners with two outs in the eighth inning, but pinch-hitter Jeff Keppinger grounded into a force out to end the threat.
"You practice plays like that in spring training and, lo and behold, you get this deep into the season and it ends up being a very big play in a game in which we were able to win," Houston manager Bo Porter said.
The White Sox have dropped 11 of their last 12 on the road and are last in the AL-Central.
"Obviously we're not in a very good position right now, but there's a lot of baseball left," Danks said.
Harrell settled down after that, retiring the next 11 batters he faced. Chicago's next hit came when Beckham singled with one out in the fifth inning. But Harrell still faced the minimum in that inning after Tyler Flowers grounded into a double play.
Porter was impressed with Harrell's work.
"I'm extremely happy," he said. "He battled and kept those guys at bay. He continued to attack the strike zone."
He threw a 1-2-3 sixth inning before running into trouble in the seventh. Dunn's sixth homer this month landed in the Crawford Boxes in left field to cut the lead to 4-2.
Danks plunked Carlos Pena with two outs in the second inning to end a career-long streak during which he retired 26 consecutive batters. Ronny Cedeno followed with a double that scored Pena to tie it at 1-all. The double was the first extra-base hit Danks had allowed in 12 2/3 innings.
He got back on track after that and sat down the next four batters, with two strikeouts, causing frustration among Houston's hitters. Jose Altuve threw his bat angrily when he struck out on a full-count to end the third inning.
Matt Dominguez singled down the left field line to start Houston's fifth. A run-scoring double by Barnes with one out that rolled into the corner of right field pushed Houston's lead to 4-1.