Left fielder Chase Headley picked up the baseball and fired home, but Atkins beat the throw sliding into home plate.
The win was the Rockies' second straight and it was also the team's second straight win in one-run games. They are 3-9 in such games.
Huston Street (1-0) picked up his first win as a Rockie even though he allowed a solo home run to Scott Hairston in the ninth to break a 6-6 tie. Bell (2-1) blew his first save of the season for the loss.
When interim manager Jim Tracy took over for the departed Clint Hurdle on Friday, he wanted better execution from his players in tight games. To get his wish fulfilled by Atkins in the cleanup hole, a guy who was getting moved around the lineup earlier this season because of his struggles, made it a little more gratifying for everyone in the clubhouse.
"I'm big-time happy for [Atkins]," Barmes said. "He came through right there in that situation. We definitely need him to do a little bit more of that and he knows that."
Atkins, who said he doesn't feel like a .190 hitter when he's up at the plate, hopes he can continue to reward Tracy's faith in him.
"It feels good to know that he's got confidence in me," Atkins said. "Obviously, I got confidence in myself. I'm just trying to come in here every day, work, try to get better and prove I belong in the four-hole. I know how important my bat is to the lineup."
While Atkins received much of the adulation, the win wouldn't have been possible without Barmes and Hawpe.
Barmes had four hits, three for extra bases, and Hawpe, in his first start since Monday because of a sore groin, had three hits, including a two-run home run in the first inning.
"We never quit, we never gave up," Barmes said. "Every time they jumped ahead, we came back and battled."
The Rockies never led until Atkins scored the winning run because of another dismal home outing by Jason Hammel.
Hammel, who was acquired in Spring Training from Tampa Bay and entered the game with a 7.63 home ERA, lasted only 3 2/3 innings and gave up six runs, five earned, including a three-run home run to Padres slugger Adrian Gonzalez in the first inning. It was Gonzalez's Major League-leading 19th homer.
"I'm not going to take anything from this tonight," Hammel said. "I put them in a big hole early."
Josh Geer (2-1), Hammel's counterpart, wasn't much better as he yielded six runs, five earned, on six hits in 6 2/3 innings.
The Padres took a 5-4 lead and knocked Hammel out of the game on Gywnn's RBI triple to center field in the fourth. David Eckstein drove in Gwynn to make it 6-4.
The Rockies scored in the seventh to cut the difference to 6-5, but they worked some two-out magic to tie the score. First, Dexter Fowler blooped a double down the left-field line followed by Barmes lacing Luke Gregerson's hanging slider down the left-field line for an RBI double.