Tipperary outscored Offaly 1-9 to 0-2 in the closing 30 minutes to leave Tullamore with the two points and move top of Division 3 on scoring difference.
Offaly had hit 1-2 in the opening five minutes of the second half to move six points up but Tipp responded to heap more misery on the Faithful, who remain rooted to the bottom of the division.
After some early shadow boxing, the game came to life on 14 minutes when a speculative Nigel Dunne effort was spilled by Evan Comerford and put into his own net by Shane O'Connell. The Faithful led 1-2 to 0-3 but Offaly's Michael Brazil and Tipp's George Hannigan were both shown straight red cards for their part in a melee as tempers flared minutes later.
Tipp centre back Robbie Kiely hit back as his powerful shot was deflected to the net to put them into a 1-5 to 1-4 lead after 28 minutes but Offaly had the better of the remainder of the half and led 1-7 to 1-5 at the break.
The hosts came out firing in the second half and hit 1-2 in the space of two minutes with the goal coming from Joseph O'Connor to put them 2-9 to 1-6 up after 40 minutes.
However, Michael Quinlivan's goal on 53 minutes put Tipp 2-10 to 2-9 ahead and capped off a sequence of 1-4 without reply as they saw out the remainder of the game while Offaly finished with 13 after Peter Cunningham picked up his second yellow card.
Scorers - Tipperary: R Kiely 1-1; C Sweeney (1f) 0-4; M Quinlivan 1-0; K O'Halloran 0-3 (3f); J Feehan, L Casey, J Kennedy, J Keane (f), K Fahey, S O'Connell, L Boland 0-1 each. Offaly: J O'Connor, S O'Connell (OG) 1-0 each; N Dunne (1f), B Allen (2f) 0-3 each; S Nally 0-2; G Guilfoyle, P Cunningham, S Doyle 0-1 each.
TIPPERARY - E Comerford 6; A Campbell 7, P Codd 7, S O'Connell 7; B Maher 6, R Kiely 7, J Feehan 8; L Casey 7, G Hannigan 5; J Keane 7, K O'Halloran 7, B Fox 7; C Sweeney 7, M Quinlivan 7, L Boland 6. Subs: K Fahey (for J Feehan 5-14 temp), J Kennedy (for L Boland h-t), K Fahey 7 (for B Maher 56), W Connors 6 (for S O'Connell 65), L McGrath (for L Casey 66).
OFFALY - A Mulhall 7; B Darby 8, J Lalor 7, S Pender 8; J O'Connor 7, P Cunningham 7, N Darby 7; E Carroll 6, D Hanlon 6; S Nally 7, G Guilfoyle 6, M Brazil 5; B Allen 7, N Dunne 7, S Doyle 6. Subs: J Walsh 6 (for S Doyle 45m), J Gethings 6 (for D Hanlon 59m), A Mahon 6 (for J O'Connor 60m), R McNamee 6 (for B Allen 65m), D Hogan (for S Nally BC 70m), W Mulhall (for N Dunne 70m).
Referee: John Hickey (Carlow).