Bibbs finished with 291 yards on 38 carries and Grayson had 302 passing yards.
"I just love the way Kapri attacks every play like it has a history and a life of its own," said Rams coach Jim McElwain. "That's really what great players do. They don't ever care what the score is. They don't care about the situation."
Colorado State did not make Bibbs available for interviews but center Weston Richburg said the back, who has 603 yards and 10 touchdowns in last two games, makes his job easier.
"As an offensive line it gives us supreme confidence that whatever look we get, he's going to be able to get a look and make a big play," he said. "I think he's a pretty special player. If we get a hat on a hat, he's going to make a big play."
Colorado State (6-5, 4-2) jumped out to a 14-0 first-quarter lead on two of Grayson's touchdown passes and New Mexico (3-7, 1-5) never got closer than three points the rest of the way.
The Lobos closed to within 45-42 at the end of the third quarter before the Rams put up three touchdowns in the fourth to put the game away.
New Mexico got 98 yards on 12 carries from Crusoe Gongbay, who stepped in for injured top back Kasey Carrier early in the game.
Colorado State piled up 649 yards of total offense and the teams combined for 1,176 total yards.
The game turned early in the fourth quarter when the Rams' defense stopped Gongbay on a fourth-and-one at the New Mexico 36.
"They did their job," McElwain said. "At the end of the day, as they were getting thundered, you could tell there was no confidence, no juice. They were just kind of hanging on. That fourth down was just a huge relief, especially for the two inside linebackers that made the hit. Aaron Davis and Max Morgan. You could feel like, 'Gosh, we finally did something.'"