The Light Blues scored five tries in posting a highest Varsity Match points total for 20 years as they triumphed 31-16.
However, Bosch also became the first player to be sin-binned in 134 years of fixtures between Oxford and Cambridge, collecting a yellow card for tipping an opposing player from a lineout.
Referee Wayne Barnes at least ensured that Bosch wasn't alone, issuing later cautions to Oxford tighthead Sean Brophy - Cambridge claimed two converted tries during his 10-minute absence - and Light Blues flanker Nic Alberts.
"It was great to score two tries, but you feel quite ashamed by being sin-binned," said Bosch.
"I was so ashamed in leaving the team for that 10-minute period."
Cambridge trailed 9-5 at half-time - and saw full-back Ian McInroy stretchered off after just four minutes - but once their forwards stepped up a gear, Oxford had no real answer.
"You can get drawn into the trap of Varsity Matches and go into your shell, but it was win or bust for us," said Cambridge's Australian skipper Ed Carter.
"To lose two players through injury and go 6-0 down after just nine minutes meant it couldn't have been a worse start for us, but when we stopped trying to play to the crowd and put some pressure on Oxford, things started to change.
"We needed to play in front of our forwards, and someone like Rudi Bosch makes an enormous difference."
Bosch apart, Cambridge scored tries through Alberts, lock Andrew Clements and wing David Akinluyi, while fly-half Jon Ufton kicked three conversions and controlled the game expertly.
"It means so much to everyone involved," said former Wasps player Ufton.
"It is a truly unique feeling in rugby because it is just one game and it means so much.
"It is right up there with everything I have achieved in the game."
Centre James Whittingham kicked three penalties and converted a late penalty try for the Dark Blues as they relinquished the trophy they won with a late try last season.
"I am very disappointed with the result. I thought at half-time we had performed pretty well and had the lion's share of possession," said Oxford rugby director Steve Hill.
"But in the first 20 minutes of the second half, Cambridge upped their game and put the pressure on.
"We had to turn our possession into points in the first half, but we weren't precise enough with the ball in hand. You can't take the credit away from Cambridge though, they played a very simple game plan and played it very effectively."