"Pretty electric," Arizona manager A.J. Hinch said. "We didn't really have an answer for it. He's a good one."
Sean Rodriguez and Jason Bartlett both had two RBI for the Rays, held hitless Friday night for the third time in the past 12 months. Price (11-3) allowed two runs and seven hits while walking one and matching his career high with 11 strikeouts.
"Yesterday was rough," Price said. "We played good ball today. We got runs whenever we needed them. That's what we've got to do."
Arizona's bid for consecutive no-hitters ended when Matt Joyce singled off a wild Ian Kennedy (3-6) to load the bases with no outs in the second. Jackson threw 149 pitches and walked eight in a 1-0 win Friday night over Tampa Bay, his former team.
Justin Upton and Chris Young homered for the Diamondbacks, who have lost 16 of their last 18 road games. Young hit a solo shot off Rafael Soriano, who pitched the ninth for his 18th save in 19 chances.
The Rays went up 1-0 in the second on Bartlett's sacrifice fly. He had a run-scoring bunt single in the seventh.
Tampa Bay scored just once -- going 1 for 8 with runners in scoring position -- during the first three innings even though Kennedy walked five, hit a batter with a pitch and allowed two hits.
"We've seen a ton of pitches over the last two days and I cannot bemoan that fact," Tampa Bay manager Joe Maddon said. "We've hit without any real luck but overall I like the idea we're maintaining our patience."
The Rays are 6 for 47 with runners in scoring position over the last five games.
Kennedy, winless in his last seven starts dating to May 19, gave up four runs and two hits. He walked a career-high nine and struck out seven in 5 1/3 innings.
"I have no idea how I go from my last outing not walking anybody to everybody," Kennedy said. "It's very frustrating. I need to figure it out by my next start."
Kennedy's previous high for walks in a game was five. The nine walks by the right-hander Saturday set a team record, breaking the mark set one day earlier by Jackson.
Arizona's starting pitcher has walked seven or more in three straight games. The Diamondbacks walked 11 and hit two batters overall Saturday.
"We got what we deserved," Hinch said.
Chris Snyder pulled Arizona to 4-2 on a run-scoring double in the seventh.
Diamondbacks third baseman Mark Reynolds struck out in all four at-bats and leads the majors with 107 strikeouts this season. He has fanned 25 times in his last 11 games.
- The Diamondbacks are leaning toward pushing Jackson's next start back from Wednesday to Friday or Saturday.
- Tampa Bay LF Carl Crawford was out of the lineup for the second straight game with a sore left shoulder and remains day to day. Crawford said the shoulder has "gotten a little better" even though he felt additional discomfort after sliding as a pinch-runner Friday.
- Arizona SS Stephen Drew (sore left knee) and C Miguel Montero (back soreness), both battling minor nagging injuries, were rested.
- Diamondbacks RHP Brandon Webb (right shoulder) threw off a bullpen mound but isn't ready to face hitters yet.