Posh fought back from 2-0 down, but were ultimately beaten by a late goal at Blundell Park in the final pre-season friendly of the programme.
By manager Darren Ferguson's own admission, pre-season can drag on somewhat. The real stuff gets underway next Saturday as Peterborough United travel to Cardiff City in Sky Bet League One action, but they will do so on the back of a 3-2 defeat to Sky Bet League Two side Grimsby Town at Blundell Park.
Posh were 2-0 down, but fought back to level thanks to goals from Cian Hayes and substitute Eddie Fox, but Sweeney popped up with a late winner after youngster Bastian Smith could only parry a long-range effort.
Chris Conn-Clarke saw a free-kick deflect wide of the target on 11 minutes, but the Mariners opened the scoring three minutes later as KABIA did well to beat George Nevett to the ball and fired past Smith.
Ryan De Havilland sent an effort wide of the target from long-range on 17 minutes while Green fired wide at the other end as both teams exchanged opportunities.
On 38 minutes, Grimsby were awarded a spot-kick following a foul by skipper James Dornelly. Charles VERNUM stepped up to convert from 12-yards.
On 73 minutes, Posh pulled a goal back as Cian HAYES, who was a threat all afternoon, cut inside and fired into the back of the net via a slight deflection.
Smith did well to keep an effort out at the other end and also repelled ex-Posh midfielder Jamie Walker as Grimsby pressed for a third.
However, it was Posh who got the next goal and ultimately an equaliser as Hayes and Dornelly linked well to provide a chance for FOX who slid in to level the scores at 2-2.
However, Posh were unable to hold on and Grimsby found a winner as SWEENEY tapped home after Smith had parried an effort from Amaluzor.
Grimsby: Auton, Sweeney, McJannet (sub Walker 65min), Tharme (sub Lavelle 77min), Rodgers, Turi, Khouri, Green (sub Warren 65min), Burns (sub Amaluzor 57min), Vernam (sub Gardner 77min), Kabia. Unused subs: Staunton, Brown.
Posh: Smith, Dornelly, Freeman (sub Fox 60min), Wallin, Nevett, De Havilland, Andrews, Conn-Clarke (sub Shofowoke 87min), Hayes, Lisbie, Lindgren. Unused subs: Westcott, Mendonca.
Attendance: 1,814 (186 Posh fans)