The Saffrons lost 0-20 to 1-15 at Cushendall but took their place in the decider ahead of Kildare by virtue of having beaten the Lilywhites.
Both counties had seven points after Kildare defeated London 1-21 to 2-14.
Carlow topped the Division by seeing off Armagh 4-24 to 0-11, the Ulster county being relegated to Division 2B.
The Orchard county are relegated on scoring difference.
The winner of the Division 2A final will face a promotion/relegation play-off against the bottom side in Division 1B.
Deaglan Murphy was prolific for Antrim in the first half as the home side went in level at 1-8 to 0-11 at the interval.
Ciaran Clarke scored the goal after 28 minutes, with Conor Johnson also getting his name on the scoresheet with a point.
The hosts nudged ahead at 1-10 to 0-11 but four unanswered points put Westmeath in front.
Further points from Murphy and Clarke brought the teams level at 1-12 to 0-15 but the visitors pulled clear to secure a two-point victory.
Antrim had defeated Kildare, London and Armagh, in addition to clinching an away draw in Carlow.
Allianz Hurling League results
Sunday 26 March
Division One A
Clare 1-22 Waterford  2-21
Cork 0-26 Tipperary  3-16
Dublin 1-16 Kilkenny  2-20
Division One B
Kerry 2-16 Offaly  1-21
Limerick 1-18 Galway 0-24
Wexford 2-24 Laois  2-20
Division Two A
Kildare 1-21 London 2-14
Antrim 1-15 Westmeath 0-20
Carlow 4-24 Armagh 0-11
Division Two B
Roscommon 2-14 Mayo 1-21
Down 2-22 Derry  2-15
Meath 3-23 Wicklow  1-16
Division Three A
Louth 1-17 Donegal 3-24
Monaghan 1-14 Tyrone 3-15
Division Three B
Fermanagh 1-14 Leitrim 4-11
Sligo 3-17 Longford  1-14
Antrim will face Carlow in the Hurling League Division 2A final next week despite suffering a first defeat of their campaign to Westmeath on Sunday.