Tony Smeeth's Trinity are staring at a relegation dog fight over the next two weeks with ties against both County Carlow and Lansdowne - the two sides below them in the table.
For Con, with the play-offs out of reach, there was little to play for but it was a deserving victory all the same, according to Smeeth.
"We didn't deserve anything from the game. It was very disappointing - we just seemed flat and Con's try was simply the difference between the sides," he admitted afterwards.
Full-back Simon Mitchell did draw them level - 3-3 - with a late penalty in the first half, cancelling out an early Pat McCarthy success.
Mitchell added a second on the restart, but Con's powerful pack dictated the final quarter. Fly-half Dan Lyons chipped over the top for right winger Rory Collins to race onto it and touch down.
McCarthy added a further penalty, but Trinity held on for their sixth bonus point - leaving them four clear of second-from-bottom Carlow.
In Division Two, De La Salle Palmerston earned their seventh win of the campaign - an impressive 21-3 shut-out of Highfield - thanks to tries from Brian Hogan, Francis Cooney and Kevin Sharkey at Kilternan.
Highfield's only points came from the boot of Conor Quaid.
Meanwhile, Banbridge and Old Wesley secured encouraging away wins in Division Three. Despite scoring three tries, Ballina lost out to Banbridge - 21-15.
Impressive centre Albert Finney kicked eleven points, while Stephen Rutledge and Gary Bickerstaff for the Ulster side.
AIB League Results: Saturday, April 2
Dublin University 6 Cork Constitution 13, College Park
De La Salle Palmerston 21 Highfield 3, KilternanScorers: DLSP: Tries: Brian Hogan, Francis Cooney, Kevin Sharkey; Cons: Philip De Barra 2, Keith TaiteHighfield: Pen: Conor Quaid
Wanderers 14 Old Wesley 23, Lansdowne Road back pitchScorers: Wanderers: Try: B Baxter; Pens: D Quigley 3Wesley: Tries: R Heap 2; Cons: D Smith; Pens: Smith 3
Ballina 15 Banbridge 21, Heffernan ParkScorers: Ballina: Tries: D Newman, T Mathison, J RuaneBanbridge: Tries: S Rutledge, G Bickerstaff; Con: A Finney; Pens: Finney 3