Goals in either half from Craig Mackie and Rob Armstrong were enough for victory after Christian Lechner had levelled with a free header for the students.
The Hive went ahead on 26 minutes when man of the match Craig Mackie finished from 12 yards after a cross from Rob Armstrong but the students levelled 12 minutes later through Lechner following a corner.
Armstrong crashed in a superb winner after 57 minutes following a break from Kareem Hassanein, finding the net with a low drive.
Division 2 side University put up a good fight thereafter, so the Hive had to guard against any slip-ups right to the end.
Stonehaven manager Martyn Rollo said: “We started strongly and should have been a couple of goals to the good in the first half, as we had three one-on-ones with the keeper but failed to score.
“But we stuck at it and I felt we were always in control and deserved to win.”
The Hive are away to Culter – 10-0 winners over Islavale in August – in the next round of the Domino’s Pizza Cup.
With some first-round ties yet to be played, the date for the second-round matches has still to be decided.
Stonehaven: Blair McIntosh, Alan Lloyd, Michael Cormack, Ludwik Metelski, Craig Lowden, Lewis Johnston, Jordan Morrice, Craig Mackie, Kareem Hassanein (sub Matthew Morris 90), Rob Armstrong, Martyn Kidd. Subs not used; Philip Low, Clark Robertson, Josh Peters.
Culter are also the opponents this Saturday at Crombie Park in the McBookie.com Superleague (2pm).
“They’ve started well so we’re expecting a tough game there but we’re confident after two fine wins,” Rollo added.
Culter are in fourth place with two wins from their opening three games.