With two minutes of normal time remaining, the Combination were 26-21 down but a Jack Easton try levelled the match before Lew Harris won the game with an injury-time touch-down.
Devonport Services back Charlie Groves had given the Academicals the lead after less than two minutes with a fine try under the posts which Ben Fallows converted.
Oaks fly-half Mac Lewis missed a penalty on nine minutes before the Combination wasted a glorious effort on the left when they knocked on over the line.
Six minutes later, the Academicals increased their advantage to 19-0 when prop Rohan Ewels touched down on the left after the students had stolen a Combination line-out.
But slowly the Combination side, with players from seven different clubs featuring, started to find their feet.
Tom Hicklin was ruled to have been held up over the line on 28 minutes before they did finally score two minutes later courtesy of captain Tom Worboys.
And eight minutes later Courtis managed to force his way over again from close range and Lewis again added the extras to put the Combination 21-19 in front.
But the students were gifted a fourth try when Fallows intercepted a pass near halfway and ran in to score and also add the conversion.
And with time disappearing quickly, the ball came out to Tavistock back Easton on the left wing and he slipped a couple of tackles to run in and scored to level the match after the students had been reduced to 14 men for 10 minutes.
The Combination sensed a winner. Easton came close again not long later following a Lewis chip over the defence and eventually the pressure did tell when scrum-half Harris took a quick tap penalty and ran in to score the winning try.
The Combination side will be back in action at Brickfields next Saturday when they host the Torbay Sharks.
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