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Both sides had important players missing due to University exams, but Caversham's superior depth of reserves was evident as a couple of injuries further reduced the Plainsmen's effectiveness.
For 28 minutes, Mosgiel competed well, until referee Jeff Clamp awarded a penalty. Well-hit by Patrick Fleming, it took an exceptional save by Mosgiel keeper Pat Howell to beat away the spot kick.
However, Mosgiel's relief was short lived as the lively Tom Jackson laced a shot from nowhere that flew past Howell and, in less than a minute, the big keeper picked another shot from his net after Fleming played a one-two through the blue ranks and finished clinically.
Down 2-0 at halftime and needing a positive start to the second spell, Mosgiel was mesmerised as Caversham interpassed from the kick-off and a multi-pass movement finished with Fleming scoring again.
Youngster Matt Brook battled in the heart of Mosgiel's defence but, with captain Mike Abbott (suspended) and Tom Bekkers (exams) absent, Mosgiel too often gave away possession.
Both Jackson and the hard-working Fleming collected hat tricks, while Robbie Deeley grabbed a brace, but the goals were a culmination of a splendid team effort that had coach Steve Fleming beaming with delight.
"Another excellent team effort, with most of our squad getting a run, and they all did well," Fleming said.
The next cup round, on July 3, will be revealed tomorrow.
Also keenly interested in the cup draw will be Roslyn-Wakari, which cruised along under the radar with a 5-3 win over Northern Hearts in Timaru.
Roslyn started in ernest, racking up a 3-0 lead from goals by Tom Connor (two) and Tim Dalman but lapses that have plagued the club allowed Hearts back into contention and at 3-2 with five minutes to go, extra time loomed.
However the elastic pace of Dalman eased management fears with two quick goals, and "since we were several first-choice players short, it was a good performance in our third away match in the cup", manager Tony Van Gorp said.
In Footballsouth Premier League matches, Grants Braes caused a minor upset by beating Queenstown 1-0. Dunedin Technical beat Northern 4-0, and in Invercargill, the Spirit beat University 2-0.