Sligo were 10 points up during the second-half but had to hang on to win by the minimum against the 14 men in front of 749 spectators in Thurles.
Kyle Cawley and Niall Murphy scored crucial first- half goals for Sligo, who made it three points from a possible four following a draw with Armagh.
Austin was stretchered off after scoring a late point and colliding with Sligo goalkeeper Aidan Devaney but the Connacht outfit suffered a big injury blow of their own when Keelan Cawley went off before half- time, with a damaged shoulder
Earlier, in the 45th minute, Feehan mistimed a shoulder on goalscorer Murphy and referee Niall Ward reached for a second yellow card for the Killenaule man.
Despite trailing 0-10 to 2-14 with 15 minutes left, Tipp could have taken something from the game.
Michael Quinlivan sent a 76th-minute free wide before Robbie Kiely’s thunderous drive from distance was deflected out for a ’45 byr Neil Ewing.
In the eighth minute of stoppage time, O’Halloran drifted his ’45 over the crossbar and when play restarted, Ward blew for full-time.
At the break, Sligo were 2-9 to 0-8 clear – Cawley netting in the ninth minute before Murphy struck eight minutes before the break.
Tipp improved in the second half and after Austin missed a big goal chance, All-Star Michael Quinlivan finished well with seven minutes left to provide the hosts with a lift.
Tipperary manager Liam Kearns said: “We’re disappointed, it didn’t go for us today – we got caught with sucker goals and getting the man sent off was a real body blow.
"I think he (Feehan) tried to him a belt of a shoulder and mistimed it a bit. He had taken a couple of clatters prior to that – was he reacting to that?”
Satisfied Sligo manager Niall Carew reflected: “We rode our luck a bit – the extra man helped us but disappointed we didn’t go 12 or 13 points up. Bigger teams would do that, put you to the sword.”
Kyle Cawley 1-2, N Murphy 1-1, A Marren 0-4 (2f), M Breheny 0-3 (2f), G O’Kelly-Lynch 0-2, A Devaney (45) & C Davey 0-1.
M Quinlivan 1-2 (0-2f), C Sweeney 0-5 (3f), K O’Halloran 0-4 (3f, 1 45), A Moloney 0-2, B Fox, P Austin & L Boland 0-1 each.
A Devaney; R Donavan, K McDonnell, N Gaughan; Keelan Cawley, N Ewing, G O’Kelly-Lynch; P O’Connor, A McIntyre; C Davey, M Breheny, J Kelly; Kyle Cawley, A Marren, N Murphy.
E McHugh for Keelan Cawley (inj., 32), S Gilmartin for O’Connor (60), S Coen for Murphy (62), J Hynes for Davey (70+4), E Connolly for Donavan (inj., 70+8).
E Comerford; A Campbell, P Codd, W Connors; K Fahey, R Kiely, J Feehan; A Moloney, M Dunne; J Keane, L McGrath, B Fox; C Sweeney, M Quinlivan, P Austin.
K O’Halloran for McGrath (h.t.), E Moloney for Fahey (50), J Kennedy for Keane (58), L Casey for Dunne (58), L Boland for Austin (inj., 69)
N Ward (Westmeath).