Jones hit three home runs in his first three at-bats and the Rangers routed the Los Angeles Angels 8-1.
Formerly a Gold Glove center fielder, Jones signed a minor league contract during the offseason to play sparingly in the outfield with the Rangers.
He hit 25 or more homers with Atlanta from 1998 to 2007, including a major league-best 51 in 2005, but ended up a dud with the Los Angeles Dodgers in '08 when he was put on the disabled list three times.
"All these years I've been playing wasn't a fluke," said Jones, who hit .156 with 14 RBIs and three home runs for the Dodgers. "Just because you have one bad year and things didn't go well ... things like that happen. I was lucky enough to put it behind me and work hard on things I had to work on. Luckily Texas gave me the opportunity to play and kept me on the team."
The Rangers got to Angels starter Ervin Santana early, with Jones hitting home runs off him in the first and third, the latter sailing over the left field pole to give Texas a 4-0 lead.
Jones added a solo shot in the fifth off reliever Rich Thompson. Taylor Teagarden and Marlon Byrd also homered for Texas.
With a chance to tie the record for home runs in a game, Jones popped out in the sixth against Kevin Jepsen and struck out against Jason Bulger in the ninth.
"I was thinking about it. I tried. I just didn't get it done," Jones said. "I'm just happy we won."
The five homers matched a season-high for the Rangers, who regained the AL West lead for the first time since June 26.
It's the second career three-homer game for Jones, who last did it Sept. 25, 2007, against Philadelphia. He's also the second player to hit three homers in a game in the last two days. Paul Konerko of the Chicago White Sox went deep three times against Cleveland on Tuesday night.
"Andrew put us on his back and everyone followed," Washington said.