The women's squad also saw action last weekend, losing 8-1 to Princeton University on Saturday and falling 9-0 to Penn on Sunday.
The Big Green men (9-6, 1-4 Ivy) entered Sunday ranked No. 9 in the country by the College Squash Association while the Quakers (5-7, 1-5 Ivy) boasted the No. 8 ranking making the match a battle for the final spot in the national championship.
In recent years, Dartmouth has not experienced much success against Penn, co-captain Daniel Wagman '10 said.
"[The victory] was awesome," he said. "We hadn't beaten Penn in the four years I've been here."
The win was also the first conference victory of the year for the Big Green. Last year, Dartmouth went 1-5 in Ivy League competition.
The Big Green got off to a slow start against the Quakers, losing two of the first three matches.
Michael Lewis '11 suffered a 3-0 loss at the No. 3 position, and No. 6 Luke Lee '12 dropped his match, 3-1. Wagman, playing at the No. 9 position, notched the opening group's only victory, winning 3-0.
"Everyone played really well today, even those who lost," Wagman said.
The next three matches with the No. 2, 5 and 8 players competing placed the Big Green in good position to win, with Dartmouth going 3-0 over its Penn counterparts.
No. 2 Nick Sisodia '12 and No. 8 Ted Schroeder '11 edged out 3-2 victories, while No. 5 Brian O'Toole '12 dominated his opponent, winning 3-1.
"Nick Sisodia had a great win," head coach Hansi Wiens said. "Both players looked really tired, and he won the last game 11-0. It was very impressive."
No. 1 Chris Hanson '13 and No. 4 Robbie Maycock '13 both pulled out wins over their opponents. Co-captain Michael Shrubb '10 lost his match 3-2, but the outcome was already decided before he took the court.
Dartmouth played Princeton University on Saturday, losing 9-0 to the No. 4 Tigers.
Teams currently set to join the Big Green at nationals are Trinity College, Yale University, the University of Rochester, Princeton, Harvard University, Cornell University and the University of Western Ontario.
"We've been getting better and better every week, and there are three weeks to go," Wiens said.
The Ivy League is well represented in the tournament field, comprising five of the eight teams currently qualified.
Last year, the Big Green entered the tournament as the eighth seed and lost 9-0 to No. 1 Trinity College en route to a first-round exit.
"I think we could do well this year," Wiens said. "Hopefully we can move up to the six or seven seed before the tournament starts."
The women failed to win their two weekend contests, but Valeria Wiens '13 notched a huge win over Princeton's top player, freshman Julie Cerullo.
Valeria Wiens entered the match ranked No. 16 individually by the CSA, so her win over No. 9 Cerullo was an impressive upset, according to coach Wiens.
Next up, the Dartmouth men will take the road for two matches on Saturday. The Big Green will take on Brown University at 1 p.m. in Providence, R.I., before facing off against Tufts University, also at Brown, at 3 p.m.
The women will also take on the Bears on Saturday at 1 p.m.