John Grose, whose previous career high was four RBIs on three other occasions, went 1-for-4 to help the Huskers, who improved to 22-5 and are off to their best start since 1987.
"Offensively, we just did what we had to do tonight," Nebraska Coach Mike Anderson said. "It was kind of Earl Weaver-type baseball with the home run and those kinds of things. It is not Nebraska style, but we got a win, so you have to be happy with that."
Robertson (3-4) went the first 5.2 innings for his second straight win, allowing three runs - one earned - on nine hits, as he matched his career high with seven strikeouts. Furnish then closed the door, fanning a career-best seven Lobos in 3.1 innings of no-hit relief for his first career save.
After spotting the Lobos (10-17-1) a 1-0 lead in the top of the first on Joe Salas' RBI single, the Huskers took advantage of the wildness of UNM starter Darren Coltrinari (1-2), who walked or hit five of the six batters he faced to take the loss. The first three Huskers reached on walks or hit batters before Jake Mullinax was plunked to knot the score at one. Curtis Ledbetter then brought home the Huskers' go-ahead run with a sacrifice fly to left before Grose's grounder two batters later plated NU's third run of the frame.
New Mexico, which saw its four-game winning streak snapped, got an unearned run in the second before the Huskers scored four times off Gaarder in the third. Singles by Mullinax and Al Smith sandwiched a hit batter to load the bases with no outs. Grose then sent Gaarder's 1-2 pitch over the fence in left for his second homer of the season and the first grand slam by a Husker in 2004.
It was the only mistake that Gaarder made, as he pitched 5.2 innings of solid relief and struck out two to keep New Mexico within striking distance.
The Lobos got their final run off Robertson in the fifth on an RBI single by Sean Murray, who had two hits, to score Josh Mader, who reached on an error. NU committed two errors on the evening and saw its streak of consecutive innings without an error end at 46.0 innings.
Matt Young was the only other Lobo with more than one hit, going 2-for-5 with a pair of runs scored.
The Huskers and Lobos conclude the series Tuesday afternoon at 1:35 p.m., as freshman left-hander Jon Klausing (0-0, 6.14) makes his first career start for the Huskers.