Rex Brothers (1-0) got two outs in the eighth to earn the win.
"Need to keep the momentum," Gonzalez said.
The momentum shifted in the sixth. Morneau led off with a double and hustled to third after left fielder Dayan Viciedo bobbled the ball on the warning track. Starter Erik Johnson retired the next two hitters and appeared he might escape the jam when LeMahieu lined a ball at right fielder Avisail Garcia.
Earlier in the game, Garcia robbed LeMahieu of a hit on a similar play. So LeMahieu figured Garcia would come up with this diving catch, too.
"Thought I was out," LeMahieu said.
Garcia leapt forward and had the ball in his glove, but when he landed, the ground jarred the ball loose, allowing Morneau to trot home with the tying run. Garcia stayed on the ground for several minutes with a jammed left shoulder before walking slowly to the dugout. The team said X-rays were negative for a fracture or a separation.
"Right now I have pain," said Garcia, who's scheduled for an MRI on Friday.
Chicago didn't ask for a video review to determine whether Garcia possibly held the ball long enough for an out.
"You really have to have a positive view of whether it was a catch," White Sox manager Robin Ventura said. "You have to have the glove around the ball to be a catch."
Chicago's bullpen melted down, giving up six runs in 2 1/3 innings. Belisario gave up five of the runs in the inning, then left with tightness in his back.
"He got the ground balls. But they just kept finding the holes," Ventura said. "And it kept going, kept going after that."
After struggling in the first two weeks of the season, Jose Abreu heated up at hitter-friendly Coors Field, where he almost wound up.
Abreu was 2 for 4 with a double on Wednesday. He had four hits in the series, including his first two homers of the season. The Rockies made a strong push to obtain the Cuban slugger in October before he signed a $68 million, six-year contract with Chicago.
Rockies manager Walt Weiss said Abreu was as good as advertised: "All the reports were this guy is a legitimate middle of the order bat. I think we saw that."
Before the game, the Rockies recalled Rutledge from Triple-A Colorado Springs, giving the team a backup for shortstop Troy Tulowitzki, who has been bothered by tightness in his right quadriceps. Weiss gave Tulowitzki the day off just so he's not "run into the ground this early."
To make room on the roster, Colorado optioned struggling right-handed reliever Wilton Lopez to Colorado Springs. Lopez has an 11.37 ERA in four games.
The White Sox open a seven-game homestand on Thursday against Cleveland, with LHP John Danks (0-0) slated to take the mound. ... 3B Conor Gillaspie had a two-run single for Chicago in the fifth. ... The Rockies have their first day off of the season Thursday before opening a three-game series in San Francisco. ... Weiss is hoping RHP Tyler Chatwood (hamstring) will be ready to rejoin the rotation on Sunday when he's eligible to come off the DL.
Copyright by STATS LLC and The Associated Press
DENVER, CO - APRIL 09: Starting pitcher Juan Nicasio #12 of the Colorado Rockies during Interleague play at Coors...