A goal from Ruairi Deane four minutes from time sealed a badly needed first win of the campaign at Semple Stadium.
Cork led by three points at the break and pushed on from there with Deane’s goal putting six points between the sides.
But Cork still had to survive a late Tipperary rally which came up just short and leaves them in deep relegation trouble.
Cork built up a three points lead when they had the breeze in the opening half on a dry evening in Thurles in front of a crowd of 1,179
But it was Tipperary who made the better start and opened up a two points lead after nine minutes thanks to a couple of frees from Conor Sweeney.
It took Cork time to settle but Michael Hurley got them off the mark with a good point after 13 minutes and Mark Collins followed up with an equaliser from the right wing shortly afterwards.
The Rebels pushed on from there with Luke Connolly edging them in front for the first time after 17 minutes with a close range free after captain Ian Maguire was fouled as he bore down on goal.
Cork increased in confidence after that and Hurley landed his second point of the night with a fine effort from the left wing to make it 0-04 to 0-02 going into the second quarter.
But Tipperary, with Steven O’Brien impressive around the middle of the field and Sweeney a good targetman up front, hit back and Jack Kennedy finished a good passing movement with a point after 22 minutes.
Brian Fox, cleared to play after having his red card from last week against Armagh rescinded, then kicked the equaliser seven minutes from the break.
But Cork finished the half strongly. Connolly kicked another free and Eoghan McSweeney supplied a fine effort from 40 metres.
And Cork took a 0-07 to 0-04 lead into the break when Paul Kerrigan pointed from 35 metres shortly before the interval.
Connolly made it double scores two minutes after the restart with his third free of the night as Cork started the second-half well.
They pushed on from there with Connolly kicked a good point from the right after being set up by McSweeney and Cillian O’Hanlon and Mark Collins made it 0-11 to 0-04 before Sweeney got Tipperary’s first score of the second-half after 49 minutes.
Sweeney followed with another point and Kevin Fahey also found the range to cut the gap to 0-11 to 0-07 going into the final quarter.
Tipperary got the margin down to three but the decisive score came four minutes from time when Sean Powter set up Deane and the Bantry Blues clubman drove the ball into the bottom left corner of the net.
Cork still had to withstand a spirited Tipperary rally but while the Premier County rattled off three points in quick succession, they were unable to get the goal they required to stave off another defeat and are now in deep relegation trouble.
Cork: Micheál Aodh Martin, Sam Ryan, Kevin Flahive, Conor Dennehy, Kevin Crowley, Thomas Clancy, Mattie Taylor, Ian Maguire, Cillian O' Hanlon (0-01), Eoghan McSweeney (0-01), Luke Connolly (0-05, 0-04f), Ruairi Deane (1-00), Michael Hurley (0-02), Mark Collins (0-02, 0-01f), Paul Kerrigan (0-01).
Subs used: Brian Hurley for Michael Hurley (54 mins), Cian Kiely for Taylor (54), Sean Powter for Kerrigan (54), Damien Gore for McSweeney (62), Ronan O' Toole for Maguire (66).
Tipperary: Michael O’Reilly, Alan Campbell, John Meagher, Emmett Moloney, Kevin Fahey (0-01), Daire Brennan, Jimmy Feehan, Steven O'Brien, Liam Casey, Liam Boland, Liam McGrath, Brian Fox (0-01), Philip Austin, Conor Sweeney (0-07, 0-06f), Jack Kennedy (0-02, 0-01 ’45).
Subs used: Dan O’Meara (0-01f) for Boland (54 mins), Ben Hyland for McGrath (62), Conal Kennedy for Fahey (66), Colm O’Shaughnessy for Meagher (68).
Referee: Fergal Smyth (Offaly).
