Jackson threw a whopping 149 pitches - a season high - and walked eight, all but one in the first three innings, in the second no-hitter in Diamondbacks' history.
"I didn't pay attention to the pitch count at the end; I didn't want it on my mind," Jackson said.
This is the third time the Rays have been no-hit since last July, including Dallas Braden's perfect game at Oakland on May 9.
Colorado's Ubaldo Jimenez no-hit Atlanta on April 17 and Philadelphia's Roy Halladay tossed a perfect game at Florida on May 29.
Jason Bartlett grounded to shortstop for the final out and Jackson's teammates mobbed him on the field. He was hit with a pie in the face by a teammate as he was doing an on-field interview.
Adam LaRoche homered off Jeff Niemann (6-2) with one out in the second, all the support Jackson would need.
Jackson (5-6) walked the bases loaded in the third but was bailed out by a stellar play by third baseman Mark Reynolds, who spun around to throw out Ben Zobrist at home plate. Hank Blalock then grounded out to end the inning.
Reynolds made another big play on a sharp line drive by Bartlett in the seventh. earlier in the at-bat Bartlett hit a dribbler that hung close to the third base line before rolling foul in front of the bag.
In the eighth, Miguel Montero threw out pinch-runner Carl Crawford trying to steal second after Carlos Pena reached on an error.
Jackson was so wild and the pitch count unusually high that the Diamondbacks had relievers warming up from the sixth inning on. Jackson pitched for the Rays from 2006-08. His only other shutout in 126 career starts came for Tampa Bay in 2007.
"It just so happened it was against a team that I played for," Jackson said.
Jackson's eight walks were a career high - he struck out six. In 2001, A.J. Burnett walked a record nine in a no-hitter for Florida against San Diego.
In the ninth, Jackson struck out B.J. Upton on three pitches. Blalock flied to left before Jackson got the final out.
Niemann struck out eight and walked two in 7 1-3 innings.
The performance by Jackson, who helped Tampa Bay make an improbable run to the World Series two years ago, overshadowed the first meeting between brothers B.J. and Justin Upton, who despite being relatively close in age had never competed with or against each other at any level before Friday.
The Uptons are one of nine sets of brothers who have played in the majors this season. About 65 relatives and friends are in town for the series, and mother, Yvonne, wore a jersey bearing the names and numbers of both above the notation: "my sons."
Diamondbacks manager A.J. Hinch joked with Justin before the game that he was tempted to post a mock lineup that didn't include the right fielder.
"I said, 'would have you been in here"' to protest, "and he said: `My mother would have been in here."'
NOTES: Crawford was out of the lineup with a sore throwing shoulder. ... Hinch confirmed Arizona had given the Florida Marlins permission to talk with 3B coach Bo Porter about their open managerial opening.
