Preston Athletic boss Jack Lynch hailed his side for their first-half showing but warned them they must cut out complacency after they were given a scare after the break.
The Pennypit club set up a William Hill Scottish Cup preliminary round two tie at home to Linlithgow Rose next month after an entertaining 90 minutes with Glasgow University.
The visitors were second best in the opening period as goals from Lewis Turkington and Jack Jardine had Preston in control, however, they grew in confidence after the break, with Sean Wilson netting what proved to be just a consolation after Brandon Archibald had netted a stunning third for the home side.
“In our last three games we have started well but in the second half we have fallen out of each game,” said Preston boss Lynch.
“I was absolutely delighted with the first-half performance. We went in 2-0 up and it should have been five or six with the chances we created.
“But then we fell out of it, we got the third goal and we thought the game was over. They then pressed on and had a couple of half chances before they scored their goal. It was nowhere near good enough in the second half, but at 3-0 up mentally players do turn off because they think the game is over.
“When you make substitutions you want them to go on and improve the team – our boys are going on and they’re are not. I can’t be too disappointed; there were some real positives then a few negatives.”
Next up is Linlithgow for a place in the first round proper and Lynch believes it is a tie his side can approach with belief.
He continued: “The team we have got here which we’ve built over the last season are good enough on their day to beat anybody. We proved that against Kelty last year in the final [of the King Cup], which we should have won [lost out on penalties after 1-1 draw].
“Linlithgow aren’t going to be any better than what Kelty were. They are a great club with good tradition. I’ve played against them loads of times over the years and I’ve actually got a decent record against them.
“We’d never underestimate Linlithgow Rose but if they underestimate us they will be in trouble.”
Midfielder Turkington got Preston off to the best possible start inside four minutes as the students were caught cold with an unstoppable effort. The ball broke to him on the edge of the box and he struck first time into the top corner. Turkington then almost netted again from even further out after he shot from the half-way line with visiting goalkeeper Andrew Smith miles off his line after running out to challenge Archibald, but he got back just in time to push over.
Archibald and Jardine then combined well on the edge of the box to double Preston’s lead as the duo played an intricate one-two before Jardine slotted past Smith.
Glasgow were moving the ball around well without troubling home keeper Craig Pennycuick, with visiting striker Donald Thomson starved of any service.
Archibald must have thought he had made it three just before the interval when he shot from point-black range from Michael McFarlane’s cut back, but Smith made a fine stop.
The midfielder didn’t have long to wait, though, as he netted on the volley just a minute after referee Ryan Oliver had resumed proceedings.
The home side rested easy on their three-goal advantage for the remainder of the second period, with Wilson netting with 15 minutes remaining for the Uni.
Preston Athletic: C Pennycuick, Austin, Ndiweni, McFarlane, Liddle, Innes, D Pennycuick, Turkington, Jardine (Carter), Archibald (Woodcock), Cochrane (Dimitrov).
Glasgow University: A Smith, Gordon, R Smith, Keith, Morgan, Van Kessel (Mitchell), Cameron (Wilson) (Small), Davidson, Thomson, Granger, Dibble.