David Power's side were always in control of the match in Mohill and ran out winners by 1-18 to 1-07 in their Group 3 clash.
Stephen O' Brien scored 1-05 for Tipperary.
The Hastings Cup is a warm-up tournament for the Championship, with three groups of four counties each.
The tournament is being hosted by last year's winners, Longford.
The winner of each group, aong with the best second placed team , will advance to the semi-finals.
Tipperary will also face Meath and Wicklow in their group campaign.
