Francisco also added a double and Edgar Renteria smacked a two-run homer for the Reds, who took two of three in this series.
Bill Bray (5-2) picked up the win after getting the final out in the ninth. Francisco Cordero shut down the Cards in the bottom of the 10th to earn his 30th save of the year.
It is the fifth consecutive season that Cordero has converted at least 30 saves.
"It means a lot," Cordero said. "It shows that I'm doing my job and have been doing my job for a long time."
Fernando Salas (5-6) was saddled with the loss after giving up the winning hit.
In the 10th, Yonder Alonso started the rally with a two-out single and Drew Stubbs walked to put runners on first and second. Francisco followed with the winning hit, ripping a single up the middle, scoring pinch-runner Chris Valaika.
The Reds had an excellent opportunity to take the lead in the eighth when Stubbs smacked a two-out double off of Marc Rzepczynski and Francisco singled to put runners on the corners, but Cincinnati was unable to cash in, as Octavio Dotel got Ryan Hanigan to ground out to end the inning.
In the bottom of the ninth, the Cards put the winning run on third when Allen Craig slapped a one-out single, advanced to second on a wild pitch and moved to third on a groundout by Rafael Furcal. St. Louis could not plate the game winner though, as David Freese ripped a line drive to left that hung up just long enough for Alonso to grab it and send the game to extra innings.
"I don't think our offense is feeling too good," Cardinals manager Tony La Russa said. "It's an aggravating or upsetting offensive day for our team. I didn't feel too good about the at-bats we took and didn't like our productivity."
Earlier, Cincinnati jumped out in front in its first at-bat. Brandon Phillips singled to center to begin the game and Renteria followed by crushing a ball from Cardinals starter Edwin Jackson just over the wall in left for a 2-0 advantage. Jackson retired the next three Reds hitters to escape further trouble.
St. Louis pulled one back in the home half of the inning courtesy of a solo- shot from Jay, his ninth homer of the season.
Despite wasting a golden opportunity in the second inning, the Cards knotted the game at two in the fourth when Gerald Laird ripped a one-out single and hustled all the way home on a triple into the right field corner by Descalso.
The Cardinals begin a crucial three-game series with the National League Central-leading Milwaukee Brewers, who currently hold a 9 1/2-game lead over St. Louis, on Monday...Jackson gave up two runs on eight hits over seven innings. He struck out eight and walked two..It was Renteria's fifth homer of the year....Reds starter Bronson Arroyo gave up two runs on 10 hits over eight innings of work. He fanned five without issuing a walk...The Reds took nine of the 15 meetings with the Cards this season.