Francis earned his first victory in more than two months, and the Rockies used two unearned runs to beat Ian Kennedy and the Arizona Diamondbacks 2-1 on Wednesday night to conclude disappointing seasons for both teams.
Francis (6-7) allowed a run on five hits in five innings in his first victory since July 27.
"We are all competitors here, whether the game means nothing or means everything," he said. "We come here to win, and that is our job."
Francis had gone 0-3 in six outings since his previous win.
"I feel like I still have that capability of being a really good pitcher for this team," he said. "I carry that confidence in every start regardless how the previous one goes. Today was a good one to finish the season on a good note."
A.J. Pollock hit his second big league home run for Arizona.
Kennedy (15-12) gave up no earned runs, striking out eight and walking none. He was 4-0 in his previous six starts.
Matt Belisle got the final out in the ninth for his third save in 10 tries.
Colorado manager Jim Tracy called it "a tremendous way to end the season" because of how much help the team got from its young players.
The Rockies took two of three to win a series at Chase Field for the first time since Sept. 20, 2009.
Despite the win, Colorado finished with a franchise-worst 98 losses in an injury-plagued season. Arizona, the defending NL West champion, finished 81-81, a fitting conclusion since the Diamondbacks were never more than four games above or five games below .500 all season.
"It stinks just as much as the last time we were at .500," Arizona manager Kirk Gibson said.
Unlike a year ago, the Diamondbacks never could put together a big winning streak.
"We ran up to .500 a couple of times, went across the line a couple of times, just never ran away from that line," Arizona's Justin Upton said. "We teetered around there all season, and that's where we ended up. It's tough when you can never get that run going."
Pollock's second home run of the season, leading off the third, barely cleared the wall over the outstretched glove of Charlie Blackmon to put Arizona up 1-0.
The Rockies took the lead with two unearned runs in the fifth. Blackmon was hit by a 1-2 pitch from Kennedy, then Jordan Pacheco singled. Wilin Rosario hit a sharp grounder to third baseman Johnson, who fielded the ball but threw wildly past second, allowing Blackmon to score and Pacheco to take third. Kennedy fanned the next two batters before LeMahieu brought in Pacheco with a single to put Colorado up 2-1.
In the eighth, Colorado's Andrew Brown contended he was hit in the wrist by a pitch from reliever David Hernandez. Plate umpire Mark Ripperger insisted the pitch hit the bat. Tracy came out and argued for several minutes before finally retreating to the dugout. Brown struck out swinging, slammed his bat to the ground and was tossed from the game by Ripperger. It was the first time Brown had been thrown out of a major league game.
Jonathan Herrera and Pacheco each singled three times for Colorado. Upton had three for the Diamondbacks to lift his average to .280 after a very slow start to the season.
Gerardo Parra was hit by a pitch from Rex Brothers leading off the Arizona ninth. He was sacrificed to second by John McDonald's bunt and took third when pinch hitter Chris Young grounded out. Pollock walked to bring up Aaron Hill, whose three-run homer with two outs in the ninth gave Arizona a 5-3 victory Tuesday night.
Belisle relieved Brothers and got Hill to line out to left to end the game.
The Arizona chapter of the Baseball Writers Association of America presented its Diamondbacks season awards: MVP to Aaron Hill, outstanding pitcher and rookie to Wade Miley, and "good guy" award to Chris Young. ... Francis' 17 victories in 2007 rank second most in franchise history behind Ubaldo Jimenez's 19 in 2010. ... Kennedy has won 36 games over the past two seasons. ... Colorado used seven pitchers in the finale.