Arenado followed with a single to shallow center that Lake fielded on the run. Gonzalez beat his errant throw home, which sailed over the head of catcher Welington Castillo.
The ball bounced off the backstop and rolled into the Rockies dugout, allowing Cuddyer to score from third.
Arenado also came home but the umpires sent him back to second, ruling the ball dead when it rolled into the dugout.
"I knew it was going to be high. It went past Welly's glove and it hit off the wall," said Jackson, who was backing up the play.
"It's just one of those unfortunate plays. Junior Lake has a strong arm, it was a hard-hit ball to center field and I knew he was coming up gunning. I wasn't able to stop the ball."
Jackson (6-11) settled down after a rough start to go seven innings, allowing five hits and four runs — three earned.
"First inning I left a couple of balls up and they took advantage," he said. "That inning right there ended up being a key factor. I was able to come back and make adjustments and get the ball down."
Jackson, whose three-game winning streak was snapped, struck out five and walked two, both in the sixth.
Chicago nearly tied it in the ninth. Castro led off with a double and scored on a groundout by Alfonso Soriano. Colby Ransom pinch-hit for Schierholtz and sent Rex Brothers' 3-2 fastball just foul down the left-field line.
Ransom walked, but Brothers struck out Lake to end the game.
The Cubs are scheduled to have Matt Garza open a four-game series in Arizona on Monday amid speculation he could be traded. Sveum said he isn't bothered by the trade rumors.
"All I know is he's pitching tomorrow. If I get a phone call and something changes, that's the way it is," Sveum said. "It's not something that consumes me."