The home county should never have found themselves in such a vulnerable position. They looked to be cruising to a comfortable victory when leading by six points with three minutes of normal time remaining.
However, Galway put in a storming finish with goal by Kevin Broderick and a point from Mark Kerins which had the deficit down to the minimum as the game drifted into injury time.
Three extra minutes were added and it could have been so embarrassing for Tipperary but for keeper Cummins' wonder save which denied Damien Hayes a possible winning goal.
It would have been very hard on Tipp had they lost this game. Apart from the opening 10 minutes, when they fell four points behind, there was only one team in it as the Premier County showed the greater hunger.
Despite playing against the wind, Galway made all the early running. There was far more urgency in their play, particularly in attack where Alan Kerins posed a lot of problems for Paul Curran.
Indeed the entire Tipp full back line struggled against the pacy Galway forwards in the opening quarter and the westerners early superiority was reflected on the scoreboard as they led 0-4 to 0-0, Kerins scoring two of those points.
Tipp moved to try and curtail Kerins by switching corner backs and it had the desired effect. Curran was far happier in the position in which he was originally picked, left corner back, and in the space of the next five minutes the sides were level after Tony Scroope put Paddy O'Brien in for a splendid goal, and Eddie Enright pointed from midfield.
Galway, after such an excellent start, began to struggle alarmingly in most sectors of the field as Tipp pushed home their advantage.
Philip Maher completely blotted out Eugene Cloonan, and with their entire half back line of Eamon Corcoran, Declan Fanning and Diarmuid Fitzgerald well on top, the westerners began to struggle for scores after their early flourish.
Eoin Kelly showed his value both as a free taker and excellent forward with a succession of points, and with John Carroll making it most uncomfortable for David Hayes at centre forward, Tipp were well worth their 1-8 to 0-8 half-time lead. It might have been more but for an excellent save by Galway 'keeper Liam Donoghue to deny Benny Dunne a goal.
Tipperary continued to dominate on the change over, with John Carroll and Tony Scroope hugely impressive in the half forward line, and by the end of the third quarter, had stretched their lead to six points.
Galway, who had performed so well against Cork the previous week, went 20 minutes without a second-half score despite playing with the wind, but a Kevin Broderick goal in the 60th minute threw them a lifeline.
Finally the pace of the game and the hurling picked up considerably following Broderick's goal and Galway had the deficit down to the minimum after Eugene Cloonan, now operating at centre-forward, pointed a free.
Tipp's response was immediate. Paul Kelly's long delivery goalwards was touched home by substitute Seamus Butler and when Benny Dunne and Eoin Kelly added points, the margin between the sides was back to six points with two minutes of normal time remaining.
Three extra minutes were added for injuries and with Cloonan's switch improving matters greatly for Galway, Fergal Healy flashed over a point. Cloonan then added another as the westerners' recovery gathered momentum.
In those hectic closing minutes the game was thrown wide open when Kevin Broderick's snap shot beat Brendan Cummins at his near post to leave three points between the sides.
Tipp were now hanging on as Galway came in search of the winning score, but Cummins made up for his earlier blunder when he saved superbly from Damien Hayes to deny the visitors a victory they didn't deserve.
: Tipperary: E. Kelly 0-8 (0-6 frees); P. O'Brien, J. Butler 1-0 each; J. Carroll, E. Enright, B. Dunne 0-2 each; P. Kelly 0-1. Galway: K. Broderick 2-1; E. Cloonan 0-6 (0-5 frees); A. Kerins, D. Forde 0-2 each; F. Healy, M. Kerins 0-1 each.
: B. Cummins; M. Maher, P. Maher, P. Curran; E. Corcoran, D. Fanning, D. Fitzgerald; E. Enright, P. Kelly; T. Scroope, J. Carroll, B. Dunne; P. O'Brien, E. Kelly, L. Corbett. Subs. T. Dunne for Corbett; S. Butler for O'Brien; C. Morrissey for Enright; D. Kennedy for Corcoran.
: L. Donoghue; D. Joyce, D. Clonan, O. Canning; D. Hardiman, David Hayes, F. More; F. Healy, T. Og Regan; M. Kerins, D. Forde, K. Broderick; Damien Hayes, E. Cloonan, A. Kerins. Subs. D. Collins for Hardiman; R. Gantley for David Hayes.
:D. Kirwan (Cork).