The Bulldogs shot 56.7 percent from the floor in the second half, converting 17-of-30 field-goal attempts, after leading by just five points at halftime.
Michael Hall had scored 14 unanswered points in the final 3:14 of the first half to cut Gonzaga's lead to 33-28. Hall led all scorers by connecting on five three-pointers, scoring 24 points to lead the Yellowjackets.
Daye, who suffered a partially torn knee ligament over the summer, showed no signs of the injury, playing 25 minutes and grabbing 12 rebounds and blocking four shots.
Heytvelt, who struggled with injuries all last season, looked healthy, adding eight rebounds and three blocks to his 15 points.
"When you see them every day, you don't always notice it," Gonzaga coach Mark Few said of both players. "Austin looked strong and he did some of the things we need him to do inside. Josh is the healthiest he's been since he was a sophomore. It's good to see him come back strong."
The pair, both 6 feet 11 with wide wingspans, combined to deny Montana State-Billings an inside game. By the midway point of the first half, the Yellowjackets were passing up inside scoring opportunities in favor of open jump shots.
The Bulldogs held a 44-31 rebounding advantage, thanks in large part to Daye and Heytvelt.
Few said Daye was behind where he would have liked to start the season, having spent two months resting the partially torn ACL. The sophomore used the time to add 16 pounds to his upper body.
"He was really making a lot of progress before he got hurt," he said. "It's too bad he lost that time."
Both Daye and Heytvelt played 25 minutes Saturday. Daye pulled down a game-high 12 rebounds and added four blocks.
Jeremy Pargo, last season's West Coast Conference Player of the Year, started his senior season with a game-high 10 assists.
Pargo initially declared himself eligible for the NBA draft, but when he learned he likely would not be a first-round selection, he opted to return for his senior season.
With junior guard Matt Bouldin adding 12 points, Gonzaga shot just under 50 percent from the floor for the game.
Gonzaga held Montana State under 33 percent from the field, and 5-of-19 from three-point range.
Montana State-Billings made its season debut under first-year coach George Pfeiffer, who spent the past two seasons as head coach at the University of Idaho, where he twice faced the Bulldogs.
The Yellowjackets, who won just once in 29 games a year ago, stayed close through the first half. They trailed by just five points with just under 18 minutes to play thanks to Hall, who transferred to Billings from Idaho, where he played for Pfeiffer.
"He's a quality, Division I-caliber player," Few said. "I think part of the problem was that we would play about 25 seconds of good defense and then get a little lost. A player like [Hall] can burn you when you do that."
At Idaho last season, Hall was held scoreless in 10 minutes against Gonzaga.
Brad Hodge was Montana State-Billings' second-highest scorer with eight points.