Down lost their perfect record after being held at Páirc Esler on Saturday night as a disputed goal just before half-time and a last-gasp free from Barry Brogan gave Tipperary a deserved 0-14 to 1-11 draw over a below-par home side in Newry.
The Munster side showed great composure, skill and that little bit of extra fitness as twice they came from behind when all seemed lost.
The Mourne men dominated the early stages and led by five points, but Tipperary hit back and the visitors netted just before the break.
The ball was adjudged to have gone over the line after a goalmouth scramble from Grogan's free.
Tipperary led 1-6 to 0-8 at half-time but Down moved ahead before Grogan levelled with a last-gasp free.