Montgomery worked a season-high, seven-plus innings and allowed one run. He took a shutout into the eighth inning.
"His future is as a starter," Cubs manager Joe Maddon said. "I think what you saw tonight is typical of what he's capable of doing over a long period of time."
Whether he remains in the rotation, goes back to the bullpen when Lester returns late this week becomes part of a six-man September rotation remains to be seen.
Montgomery says he will do whatever the Cubs want.
"I'm going to assume that I'm going to be asked to start again, and if it changes, it changes, and I'm going to be able to adjust from there," he said. "My focus is towards keeping myself physically ready to go and mentally ready to go for the next month."
Montgomery (5-6) struck out four, walked none and allowed six hits. He also had a hit and scored a run in the opener of a three-game series at Wrigley Field.
Chicago (70-60) has won two of its past three. The Pirates (63-69) saw a two-game winning streak end and fell eight games behind the National League Central-leading Cubs.
Pirates right-hander Trevor Williams (5-7) worked five innings and took a third loss in his past four starts. He gave up two runs on six hits and three walks while striking out four. Williams is now 1-2 in his career against Chicago, all this year.
"We weren't able to create much offense, but I thought Trevor pitched a very gritty game, very gutsy game," said Pirates manager Clint Hurdle. "We put ourselves in a position to be in a closer game, but we couldn't get outs when we needed to."
Ahead 2-0, the Cubs loaded the bases in the seventh and scored three runs on Alex Avila's two-out infield single. Kris Bryant came home on the hit, and Jon Jay and Ian Happ then scored on two Pirates throwing errors on the play to make it 5-0.
Montgomery's shutout bid ended in the eighth with Jordy Mercer's leadoff home run to left, Mercer's 12th of the year. Montgomery was replaced by Carl Edwards Jr., who worked the rest of the inning.
Cubs closer Wade Davis worked a 1-2-3 ninth.
Jason Heyward went 2-for-4, Bryant was 1-for-3 with two walks, and Happ went 1-for-3 with a walk and an RBI.
Mercer went 3-for-3 for the Pirates, and David Freese finished 2-for-4.
Happ gave the Cubs a 1-0 lead in the second. Anthony Rizzo lined a leadoff double to right, and Happ bounced an RBI single up the middle to drive him in with no outs.
Cubs shortstop Javier Baez turned in the defensive gem of the game in the third inning, hitting the dirt as he stopped a Jose Osuna liner and quickly picking himself up for a throw that barely beat the runner at first.
The Cubs made it 2-0 on a Rizzo sacrifice fly to deep center in the fifth.
Montgomery reached on an infield single and advanced to third on Tommy La Stella's one-out base hit to right. Williams walked Bryant to load the bases for Rizzo, who knocked in the run with his fly ball.
"They made me pitch to them in some tough situations," Williams said. "There's a few pitches that I missed and got hurt on, but I thought we did a great job sticking to the game plan."
NOTES: The Pirates shuffled their roster, placing INF Adam Frazier (strained right hamstring) on the 10-day disabled list, recalling OF Jordan Luplow and RHP Dovydas Neverauskas from Triple-A Indianapolis and sending RHP Johnny Barbato to Indy. ... The Pirates send RHP Chad Kuhl (6-9, 4.52 ERA) against Cubs RHP Jake Arrieta (13-8, 3.49) in Tuesday's middle game at Wrigley Field. ... Chicago 1B Anthony Rizzo has reached 30 homers for the fourth straight season. ... Cubs LHP Jon Lester (lat, shoulder) threw a 47-pitch simulated game at Wrigley Field on Monday and is on target for a late week return off the disabled list. ... Cubs organist Gary Pressy entertained in his 2,500th consecutive game on Monday, a run of nearly 31 seasons.