The Astros have posted three straight shutouts for the first time since 1986, they said in citing research by the Elias Sports Bureau.
The season-ending series between NL Central clubs marks the first meeting of 100-loss teams in the majors since 1962, when the Cubs played the New York Mets.
The Astros (55-106) won for the fifth time in six games. They have already matched last year's franchise-worst loss total.
"The team won three in a row. That's the way we're looking at it," Norris said. "We're trying end this thing strong and play it all the way through."
Norris (7-13) scattered four hits and won back-to-back starts for the first time since May.
Norris pitched out of several sticky situations. He put runners in scoring position with less than two out in four consecutive innings but didn't allow any runs to cross home. Norris struck out Luis Valbuena and Welington Castillo with runners on second and third to end a fourth-inning threat.
The 27-year-old endured a 19-start winless stretch before winning his last two. Four Astros relievers held the Cubs hitless over the final three innings. Wilton Lopez worked the ninth for his 10th save in 13 chances.
"I can't say enough about our bullpen today,' interim manager Tony DeFrancesco said.
Houston is 15-14 since Sept. 1 and has won its first road trip of the season with a 4-1 record. The Astros are playing their final series in the NL before moving to the American League in 2013.
"Either way, we're going to finish strong," DeFrancesco said. "We're going to finish .500 for the month, and we're really excited about the future, what's going on for next season."
DeFrancesco said Wednesday's finale will be special. He managed the Astros' Triple-A team before he took over for the fired manager Brad Mills on Aug. 19.
"If everybody signs the lineup card, it will be a special memory," DeFrancesco said. "I'll get it framed, and move onto a new chapter in my life. This has been a very special chapter."
Chris Volstad (3-12) took the loss for the Cubs, who fell to 60-101.
Castro hit his sixth homer of the year, sending a solo shot into the right-field bleachers with two outs in the second inning. Justin Maxwell reached on shortstop Starlin Castro's 27th blunder of the year following the home run, and came around to score on Tyler Greene's single.
Volstad was otherwise effective, striking out six and walking none in seven innings.
The Cubs were blanked for the 16th time this season. It's the second time they have been shutout in back-to-back games, the other instance coming July 21-22 at St. Louis.
"Not a lot of quality at-bats again, left some guys on, striking out with guys in scoring position again," Cubs manager Dale Sveum said. "It's kind of typifying the whole season, these last two nights swinging the bats."
Astros OF Scott Moore left in the second when he was hurt diving for Castro's shallow popup. The team announced he had irritation in the AC joint in his left shoulder. ... Astros 2B Jose Altuve left in the fifth with discomfort in his left groin. Neither player is expected to play Wednesday. ... The Astros start Edgar Gonzalez (3-1, 4.15 ERA) on Wednesday. Travis Wood (6-13, 4.39) goes for Chicago. ... The Astros are one victory short of 4,000 wins in franchise history. They are 3,999-4,133 in 51 seasons.