The meet was held at Princeton's 8K course at West Windsor Fields.
Geoghegan continues his outstanding junior fall with a fifth-place finish in 23:54.2, while Royer made up for a disappointing 2011 Heps by finishing sixth in 23:57.6.
Both earned All-Ivy First Team recognition for their showings Saturday.
The collective unit of the Big Green earned third place with 77 team points, edging out Cornell in fourth with 83 points. For the third straight fall, the Princeton men came away with the title, recording an impressive 26 points on the strength of Chris Bendtsen and Alejandro Arroyo Yamin taking the top two spots. Columbia was second with 58 points.
"Both those teams (Princeton and Columbia) are nationally ranked, so beating the rest of the league was huge for us," Herbert Chase Head Coach Barry Harwick '77 said. "As a team, it was our best race of the season and we still have yet to really put everything together, which is a good sign.
"At this meet a year ago, Phil (Royer) wasn't able to finish. He deserves a lot of credit for coming back this year determined and earning first-team recognition."
Junior Steve Mangan ran his best race of 2012, taking 17th in 24:14.8.
Sophomore Dylan O'Sullivan earned points at the league's championship meet for the second straight year as he crossed the line 23rd overall (24:35.6). Senior Jonathan Gault was the fifth member of the Green and White in the scoring, registering 26 points as he crossed in 24:30.3.
Just outside the scoring were freshman Curtis King (29th, 24:32.3) and junior Henry Sterling (37th, 24:49.3).
Now, Dartmouth will shift its focus and attention to preparing for the NCAA Regional meet in New London, Conn., on Friday, Nov. 9.
1) Princeton, 26
2) Columbia, 58
3) Dartmouth, 77
4) Cornell, 83
5) Harvard, 131
6) Yale, 158
7) Penn, 185
8) Brown, 223