South African forwards Rudi Bosch and Nic Alberts led the way with close-range touchdowns, before tries in three second-half minutes from lock Andrew Clements and wing David Akinluyi finished off Oxford.
Fly-half Jon Ufton kicked three conversions, including the extras following Bosch's second try just before full-time, and Oxford could only manage a late penalty try and 11 points from centre James Whittingham as Cambridge wiped out a four-point interval deficit to record their biggest Varsity win since 1997.
Oxford were crushed by a heavyweight Cambridge pack that tightened its grip when Dark Blues prop Sean Brophy followed his opposite number Bosch into the sin-bin.
With Brophy absent, Cambridge sealed the deal through a quickfire try double, and there was no way back for Oxford in front of a 38,733 crowd.
Cambridge banked on experience in their victory quest, fielding three 31-year-olds in Bosch, Ufton and lock John Blaikie, but Oxford were determined not to relinquish their Varsity crown under the captaincy of hooker Andy Dalgleish.
The Light Blues suffered an immediate injury setback when full-back Ian McInroy was stretchered off after a sickening clash of heads with Oxford flanker Doug Abbott.
McInroy was replaced by Steffan Thomas, meaning a positional switch inside four minutes for skipper Ed Carter, who moved from centre to full-back.
But Cambridge's nightmare start continued when Thomas went off five minutes later, having tried to tackle Whittingham, which meant another enforced change as coach Tony Rodgers sent on Northern Ireland-born centre Paul Magee.
Whittingham booted Oxford ahead through a short-range penalty, and Cambridge just could not settle, a fact emphasised when wing Charlie Desmond tried to run from deep, but was hauled down and then penalised for not releasing possession, allowing Whittingham his second successful kick.
Thomas returned to the action with Cambridge 6-0 adrift, and it took the Light Blues 20 minutes to establish any kind of territorial threat, but they made a spectacular arrival in Oxford's 22.
Clements soared high to claim quality lineout ball, and with Oxford's defence non-existent, a 20-metre drive resulted in Bosch touching down for the opening try on his fourth Varsity Match appearance.
Cambridge, following their early problems, began to exert dominance up front, but some poor options among the backs helped save Oxford from conceding a second try as they were stretched defensively.
However, the Light Blues made life tough for themselves as half-time approached, when Bosch created a slice of unwanted Varsity Match history.
The South African tipped Oxford number eight James Jones from a lineout, and referee Wayne Barnes brandished a yellow card, making Bosch the first player to be sin-binned in 134 years of Varsity fixtures.
Whittingham then completed his penalty hat-trick, edging Oxford into a 9-5 interval lead.
Cambridge, despite being a man down, regained the advantage within four minutes of the restart when their forwards again laid siege to Oxford's line and Alberts claimed an inevitable score.
Ufton again failed to convert, but the try put Cambridge one point ahead as Bosch returned just in time for another relentless drive into the heart of Oxford's defence.
The Oxford scrum also showed signs of creaking, and referee Barnes yellow-carded Dark Blues tighthead Brophy for a technical infringement as Cambridge attempted to press home escalating set-piece authority.
Cambridge encountered some fiercely committed Oxford tackling, but the Dark Blues could only hold out for five minutes in Brophy's absence.
Clements powered over for Cambridge's third try on 57 minutes, then Akinluyi charged down Oxford full-back Anthony Knox's kick on halfway before gathering a kind bounce and sprinting 50 metres for the clincher.
Ufton at last found his range to convert both tries and send Cambridge clear at 24-9 in front, leaving Oxford with a mountain to climb during the closing quarter.
Predictably, though, Oxford could make little impression as Cambridge easily closed them out despite seeing Alberts yellow-carded and conceding a late penalty try before Bosch's second score avenged an agonising last-gasp defeat 12 months ago.