Norris scored on a passed ball with two outs in the seventh inning, and the Oakland Athletics beat the Chicago Cubs 1-0 on Thursday.
He also put the tag on Starlin Castro trying to score, threw out a runner at second and called Dan Straily's best game as a major league pitcher.
"He was pretty much the hero of the day," Straily said. "Even when I tried to shake him off he put down the same finger and set up. We were on the same page all day—his page really and it was a good one."
Straily (5-2) pitched seven innings of one-hit ball after being recalled from Triple-A Sacramento earlier in the day.
"Even if I didn't have my best stuff I was going to give it everything I had," said Straily, who struck out six and walked three. "My slider was not as sharp as it's been but it was good enough."
Ryan Cook pitched the eighth and Grant Balfour finished for his 21st save in 21 chances, completing the two-hitter. Balfour has converted 39 straight save opportunities dating to last year, one off the team record held by Dennis Eckersley.
Norris set up the only run of the game when he walked with two outs in the seventh and went to third on Seth Smith's single.
Oakland then sent Eric Sogard to the plate to hit for Adam Rosales, and Matt Guerrier threw an 0-1 pitch to the outside part of the plate.
"I saw it go between his legs," Norris said. "You know the guy may bounce one in the dirt because he can't throw all fastballs and that's what you look for: any chance to score. I tried to kick it into another gear just in case the ball bounced right back to him but fortunately it kicked off to the right."
It was the first appearance for Guerrier (2-4) since he was acquired in a trade with the Los Angeles Dodgers. Castillo, catching Guerrier for the first time, wasn't sure what to expect from the pitch that got away.
"He made a good pitch," Castillo said. "I just didn't get a good read on it and it went between my legs."
Cubs starter Travis Wood allowed three hits over six innings in his third consecutive no-decision. He is 0-3 in his last six starts despite a 2.58 ERA over that stretch.
"You have to keep battling every single day," Wood said. "Their guy pitched awesome. He kept us off balance and off the scoreboard. I have to find a way to win these games."
The Cubs had a chance to score in the fourth but Yoenis Cespedes cut down Castro trying to come home from second on Alfonso Soriano's single to left field. Soriano was later thrown out by Norris attempting to steal second, ending the inning.
"I didn't think, when the ball was hit, he had a chance," A's manager Bob Melvin said of Cespedes. "That was a spectacular throw. I don't know if there's a left fielder with a stronger arm."
Castro walked to open the inning and advanced when Nate Schierholtz grounded out.
"That was perfect throw," Norris said. "It took one bounce and hopped right to my stomach."
The A's also had a potential run thrown out on the bases. Chris Young singled with one out in the seventh but was caught stealing by Castillo.
Pedro Strop pitched a scoreless ninth in his Cubs debut as the team matched a franchise record for players used before the All-Star break with 41. The Cubs also extended their franchise record by using 23 pitchers before the break.
NOTES: Cubs OF Brian Bogusevic left after the top of third inning with left hamstring tightness. ... The A's optioned C Stephen Vogt to Triple-A Sacramento to make room for Straily. ... The Cubs announced that RHP Carlos Villanueva (2-4, 3.45 ERA) will start Sunday's game against Pittsburgh, filling the spot vacated when RHP Scott Feldman was traded to the Baltimore Orioles. Villanueva started the year in the rotation, but went to the bullpen when RHP Matt Garza came off the disabled list. ... RHP Jeff Samardija (5-7, 3.34 ERA) will take the mound Friday night against the Pirates at Wrigley Field. He's 4-2 with a 1.56 ERA against the Pirates in his career, though just 1-2 against them this year. ... LHP Tommy Milone (7-7, 4.17 ERA) will start for the A's in Kansas City. He's 1-2 with a 5.96 ERA over his last four starts. ... According to Sports Features Group, the last time the Cubs lost a 1-0 game, with the lone run scored on a passed ball, was July 1, 1962, in Milwaukee.