Dower switched his focus to the inside in the second half, and Gonzaga pulled away for an 80-68 victory on Saturday.
Dower led all scorers with 22 points, including 14 in the second half.
"In the second half I decided to go to my inside game more," the 6-foot-9 Dower said. He made 7 of 9 from the field in the second half to help the Zags overcome a slow start.
"We played really well tonight," Dower said. "Guys were aggressive in getting to the rim. That helped us out."
Gerard Coleman added 21 and Kevin Pangos added 15 points for Gonzaga (8-1).
Gonzaga led 31-30 at halftime, after shooting just 35 percent in the first. They shot 64 percent in the decisive second half.
"We got used to what their style of play was going to be," Pangos said of the Aggies. "We executed a lot better in the second half."
Coleman came off the bench to sink 10 of 19 shots.
"He was great at getting to the rim," Pangos said. "He can finish so many different ways."
Daniel Mullings scored 17 points for New Mexico State (7-4), which lost its third straight game. Tshilidzi Nephawe added 13 points.
Gonzaga leads the nation in field goal shooting at 55.8 percent, but was cold at the start and couldn't put the Aggies away until the final minutes. They shot just 48 percent, but won the rebound battle 45-30.
"We had a goal to beat them on the glass and we did that," Gonzaga's David Stockton said. "That shows you what our team is all about."
Przemek Karnowski had nine points and nine rebounds for the Zags.
In a seesaw first half, New Mexico State's Sim Bhullar had a tip-in and a stuff as the Aggies built a 10-4 lead in the opening minutes. The Zags made just two of their first 10 shots.
Dower scored six points as Gonzaga came back to tie the score at 16.
Consecutive baskets by K.C. Ross-Miller put the Aggies ahead 24-19.
Gary Bell Jr. and Drew Barham scored to keep Gonzaga close, and a put-back by Coleman gave the Zags a 29-28 lead with 3:06 left in the first. It was their first lead since the opening two minutes. Coleman, who had 10 points in the first, added another basket for a 31-28 lead.
New Mexico State was scoreless for more than five minutes before Mullings' basket at the buzzer left the Aggies trailing 31-30 at halftime.
"We had them in the first half right where we wanted them," New Mexico State coach Marvin Menzies said.
Gonzaga made just 13 of 37 shots in the first half and missed all five of its 3-point attempts. But 14 offensive rebounds led to 13 second-chance points. New Mexico State shot 43 percent in the first.
"When you have a deep, balanced team, they were able to overcome our game plan with putbacks," Menzies said of Gonzaga's 18 offensive rebounds in the game. "We didn't anticipate their rebounding would be so efficient."
Gonzaga scored the first seven points of the second half, six by Dower, for a 38-30 lead. Pangos hit Gonzaga's first 3-pointer of the game for a 41-33 lead with 16:12 left.
A jumper by Ross-Miller brought the Aggies within four points, but Coleman made three unanswered baskets for a 49-39 Gonzaga lead. While Gonzaga was finding the range, New Mexico State made just three of its first 15 shots in the second.
Pangos' 3-pointer gave Gonzaga a 53-41 lead. The Zags kept a double-digit lead most of the way after that.
The Bulldogs average 91 points per game, fifth in the nation. ... This was the first meeting between the programs. ... New Mexico State has not beaten a ranked team since defeating Nevada in 2007. ... New Mexico State's next game is at No. 2 Arizona on Wednesday. ... Gonzaga is 125-8 in the McCarthey Athletic Center since the building opened in 2004.