Tipp led 2-8 to 0-6 points at half time but were outscored by 2-9 to four points in the second half.
At full-time it finished Tipperary 2-12 Wexford 2-15.
Tipp manager Peter Creedon credited Wexford's second half performance.
Elsewhere, Tyrone have been relegated from Division 1 after drawing against Kerry by a 1-14 to 0-17 score line.
Dublin beat Monaghan to take second spot, but both teams advance to the semi-final stage.
Mayo and Donegal drew 1-9 to 0-12 but it’s Donegal who advance to the knockout round.
Top of the table Cork lost to a relegated Derry by 2-15 to 1-11.
In Division 2 Roscommon beat Westmeath 2-13 to 0-12 to gain promotion to Division 1, relegating their opponents in the process.
Down also confirmed their promotion with a 3-12 to 1-15 win over Laois.
Kildare have been relegated after 3-12 to 1-12 defeat in Galway.
Meath beat Cavan 0-14 to 0-12.
Fermanagh and Armagh were already guaranteed promotion from Division 3.
Both lost to Clare and Sligo respectively.
Wexford have been relegated despite fighting back to beat Tipperary 2-15 to 2-12 and Limerick beat Louth by 2 points.
Louth have also been relegated.
Longford and Offaly have been promoted from Division 4
Longford beat Carlow 1-18 to 1-12, Offaly defeated Antrim 1-13 to 1-7 and London beat Wicklow 2-8 to 0-12.
In Division Three next season it will be Clare, Limerick, Tipp, Kildare, Westmeath, Offaly, Longford, Sligo.
