"This game was ugly from the beginning," Alford said.
The victory gives the Lobos (25-4, 12-2 Mountain West) their fifth conference championship in the last six seasons.
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"If you go into our locker room, we don't hang up just pictures," Alford said. "We hang up championship pictures."
And this victory was similar to many other Lobos wins this season, especially at home, where they were perfect.
"To be able to win every home game is something special," Alford said. "It's been a very consistent team in regards to toughness and the ability to play hard and to do it together and to do it unselfishly."
New Mexico scored big from the foul line, going 21 for 27. And the Lobos limited Wyoming's opportunities from the line, holding the Cowboys (18-11, 4-11) to just seven foul shots.
The Lobos also played gritty defense on the Cowboys, who shot 16 of 57 from the field. New Mexico was particularly effective guarding the 3-point arc in the second half, holding Wyoming to 2 of 11.
"There is nobody that plays tougher that the Lobos," Alford said. "This team is downright nasty."
The Lobos have had a historic season defensively, he pointed out.
"It's going to be only the second time in school history, since the peach basket went up, that we are going to hold teams to under 40-percent shooting in back-to-back seasons and under 60 points per game," Alford said.
Offensively, New Mexico was able to exploit its big front court, with post Alex Kirk scoring 15 points with nine rebounds and forward Cameron Bairstow adding 13 points while also grabbing nine boards.
The pair also dominated Wyoming forwards Leonard Washington and Larry Nance Jr., who combined for four points and 12 rebounds.
Still, Wyoming was in the game, pulling within 34-31after a Derek Cooke Jr. basket with 11 minutes left.
The Lobos were in the middle of a drought from the field as they went almost nine minutes without a basket.
"We had the game exactly where we wanted," Wyoming coach Larry Shyatt said. "If we dropped a couple shots, or perhaps got a foul or two, I thought we were right there to win the game. Especially when it was three or four points."
While New Mexico went cold from the field, it was also marching to the line and stifling Wyoming.
The Lobos hit 7 of 9 on foul shots while building a 13-3 run that put the game away.
"They keep each other accountable on the floor," Alford said. "They help each other defensively. They move the ball and they do so many
things to keep each other accountable. Unselfishness. There is nothing better to say about a group of young men and a team then to talk about unselfishness. And they've been doing that all year long."