"I don't know if she was a D-back fan, but I think she is now," Parra said.
Before Parra went to bat in the sixth inning against Eric Stults, an elderly woman in the front row shouted out a word of encouragement. He went over and told her to touch his bat for good luck.
Parra also told her if he got a hit, she could keep the bat. After he connected on a 2-1 fastball to give the Diamondbacks a 6-0 lead, he retrieved the bat from the bat boy and gave it to the woman.
He said he looked for her before his last at-bat in the ninth but she was gone.
Paul Goldschmidt and Miguel Montero also homered to help Cahill in his second career shutout and complete game. His other came with Oakland on Aug. 2, 2010 in a 6-0 win against Kansas City when he threw a three-hitter.
Arizona backed the sinkerballer with four double plays.
"Defense helped out a lot," Cahill said. "I got some ground balls at guys. I tried to attack the zone because they have been aggressive all series, so I tried to take advantage of that."
Cahill, born and raised in Vista about 40 miles north of San Diego, won for the first time in six starts, striking out five and walking three.
Manager Kirk Gibson applied a little more pressure, too. He walked into the clubhouse after Saturday night's game and approached Cahill.
"I told him we needed him to go eight innings," Gibson said.
"I was kind of caught off guard. It kind of scared me a little bit. He was trying to see how I responded. I kind of went, 'Huh?' "
Cahill's effort followed the outstanding eight-inning outing by Daniel Hudson in Saturday night's 4-2 win.
"We're going great this time through the rotation," Gibson said. "This is what we were looking for. We were wearing out our bullpen. It's time for them to be able to go deep in the game."
Goldschmidt hit a solo homer to extend his career-best hitting streak to 12 games, during which he has hit four of his six home runs. Montero and Parra each hit two-run homers and Arizona won for the third time in four games to salvage a split of its six-game road trip.
Goldschmidt's homer to right field in the second inning barely carried to the top of the scoreboard where it caromed into the stands to give Arizona a 1-0 lead.
Montero's two-run blast to center capped a three-run sixth in which San Diego's sloppy play contributed to the first run. Parra connected a after a leadoff walk in seventh.
San Diego, which has the majors' worst record at 18-37, has lost 11 of 13.
Cahill faced the Padres for the second time in career. Acquired from Oakland during the offseason, Cahill made his Diamondbacks debut in San Diego on April 10. Even though he didn't get the decision in a 4-2, 11-inning win, he allowed just one run in six innings.
The Padres squandered their best scoring chance after a leadoff triple by Logan Forsythe in the fifth. With one out and Stults at bat, Forsythe took off down the third-base line on what appeared to be a squeeze.
But on a high fastball that was away and out of the strike zone, Stults squared to bunt but he never made an attempt. Forsythe was tagged out easily by Montero, the catcher.
"It was kind of up and away and I pulled back a little bit," Stults said. "I've still got to make an effort at that. That was on me."
Stults (1-2) allowed all three home runs and gave up a season-high six runs on seven hits over 6 1/3 innings. The lefty struck out four and walked two.
Game notes Cahill was 1-5 with a 4.69 ERA in his previous eight starts. ... San Diego CF Will Venable left the game in the third inning after straining a right oblique muscle. ... Padres LF Carlos Quentin was out of the lineup for the first time since he made his season debut on Monday and started all five games since coming off the DL. Quentin, hitting .474 with three homers and seven RBIs, had right knee surgery on March 19. ... Diamondbacks RF Justin Upton was back in the lineup after getting Saturday off following a 3-for-20 slump over the previous five games. ... Arizona SS Stephen Drew, out since July with a broken ankle, played all nine innings in extended spring training game on Saturday, playing consecutive games for the first time in his rehab. ... LHP Joe Saunders (3-3, 3.61 ERA) opens Arizona's three-game series at home Monday night against Colorado and LHP Christian Friedrich (3-1, 5.59). ... RHP Anthony Bass (2-5, 3.42) will be on the mound Tuesday night when the Padres host San Francisco and RHP Tim Lincecum (2-6, 5.82) in the opener of a three-game set.