Both sides were missing regular players, and Caversham certainly missed some stability in defence and the feisty energy of Andrew Ridden.
Caversham coach Tim Horner gave his side only a "pass mark'' for a performance that earned the win but had too many passes go astray, especially in the attacking third.
It took a 25th-minute free kick drilled in low by Seamus Ryder - aided by team-mates jumping over the ball - for keeper Morris to be beaten, and Caversham settled down at 1-0.
Keeper Morris actually trialled with Caversham in pre-season, but eventually opted for University and literally had his hands full as he made several top full-length saves, in contrast to his near redundant opposite number, Liam Little.
Varsity coach Darren Hart praised the custodian and, despite being disappointed at the actual score, he was more than happy with some player performances, especially going forward.
"I thought that we might have got something from the game,'' he said.
"We did not make many breaks, but had a couple of decent chances that might have gone our way.''
Certainly there were the usual entertaining phases of tricky play by the likes of Warkina Tujuba, some driving midfield play by Ewan Bakker and stiff defence by Joe Clark, but the player who stood out was Steven Walker, who worked tirelessly in the heart of midfield.
Caversham seems to have discovered a replacement for the giant throw-ins made by Tom Jackson, and possibly Sam Cosgrave hurls the ball even further into the opposition goal area,Yet for all the ball possession, pace and territorial advantage, Caversham looked rusty on the less-than-perfect pitch, and the sea breeze blowing hard at the Bayfield inlet did not help.
The back four of Mitchell Carter, Craig Ferguson, Rhys Henderson and Sam Cosgrave were rarely in trouble, and both Jared Grove and Michael Hoggan were effective in central midfield.
Striker Lewis Jackson worked hard, stole the ball a few times and created breaks, but was left scoreless.
It was the other half of Caversham's attack that struck with 10 minutes to go as Grove flighted a free kick goalwards and Sam Collier stole in to nod what looked like an unopposed goal.
Referee Calvin Berg then reduced University to 10 men when he sent off Matt Ward for an over-enthusiastic tackle.
After scoring an earlier hat-trick for the Caversham reserves, Callum Flaws went on with minutes remaining and was the man on the spot to force the ball in from close range and wrap up Caversham's 3-0 win.
At Sunnyvale, Mosgiel served notice of serious championship intent with a 6-0 thrashing of the young Green Island side.
Roslyn-Wakari also had a sound 3-0 win over Northern, striker James Govan scoring twice after a lengthy absence through injury.
Another round of games will be played on Monday.
