The Eagles (2-1) led by as many as 13 points in the second half and were able to beat back multiple Lobos runs down the stretch.
Hugh Greenwood led the Lobos (2-1) with 24 points.
New Mexico kept it close despite playing most of the final 20 minutes without point guard Cullen Neal, who left with a sprained left ankle. The Lobos bench also chipped in 22 points.
Boston College looked to be pulling away after a 9-2 spurt gave it a 47-34 lead with just under 17 minutes to play.
The Lobos appeared to gather themselves with an 8-0 run of their own to get back within 47-42.
That momentum dissipated, though, after a pair of turnovers contributed to seven straight Eagles' points that put New Mexico back in a double-digit hole.
The Lobos tightened up in their zone defensively and turned it into points, trimming Boston College's lead all the way down to four points with just over a minute to play.
But Boston College was able to connect on enough free throws to preserve the win.
Both teams were virtual mirrors of one another statistically in the opening 20 minutes.
The only major difference was how much better Boston College shared the ball, spreading around nine assists.
The Lobos managed only four assists, while relying heavily on Greenwood to providing scoring when their offensive sets stalled.
The Eagles were also a lot more patient, piling up 16 points in the paint.
New Mexico: The Lobos are now 10-11 all-time against the Atlantic Coast Conference.
Boston College: The Eagles had 21 points off 17 Lobos turnovers.
The Eagles advance to play the winner of George Mason and West Virginia on Friday. The Lobos will play the loser of that matchup in the consolation round.