Hannigan got down to save from the substitute with time almost up and his side holding a slender two point advantage.
Ruairí Ó Coileain contributed seven points as last year’s beaten finalists safely negotiated the opening hurdle.
Meath, with five senior panellists, had the edge throughout though it was anything but an impressive win,
With Shane Dempsey and Ray Connellan in excellent form, Westmeath led 1-5 to 1-4 at the break.
They led 0-4 to 0-2 after 21 minutes but then senior star Eamon Wallace went on a mini scoring spree for the hosts with a goal and two points in a five minute spell.
That left Meath leading 1-4 to 0-4 but the Lake County finished the half strongly with a penalty goal from Connellan before the same player hit the lead point.
With Ó Coileain showing good accuracy from placed balls, Meath went three clear by the 50th minutes.
Points from Connellan and sub Michael Monaghan reduced the deficit to the minimum before another sub, Oisin Reilly, shot the insurance score for Meath.
Westmeath finished with 14 men following the late dismissal of Ryan Caffrey.
Scorers for Meath: R Ó Coileain 0-7 (5f), E Wallace 1-2, O Reilly 0-1.
Scorers for Westmeath: R Connellan 1-3 (1-0 pen), S Dempsey 0-4, M Monaghan 0-1.
MEATH: J Hannigan; M Flood, G McGowan, L Ferguson; S Dowling, B Power, S McEntee; A Flanagan, P Harnan; B Duggan, R Ó Coileain, J Wallace; S Lenihan, K Ryan, E Wallace.
Subs: C Rooney for Duggan 35, B Dardis for Ryan 45, O Reilly for J Wallace 47, C Carton for McEntee 60.
WESTMEATH: B Doyle; B Sayeh, I Ilunga, R Gorman; K Daly, R Caffrey, D King; T Watts, G Delaney; D Conway, R Connellan, J Barrett; S Corcoran, G Leech, S Dempsey.
Subs: TJ Fox for Barrett 33, M Monaghan for Leech 46, A Curley for Conway 51, J Madden for Watts 51, D McDermott for Delaney 59, Conway for Sayeh 59.
Referee: F Smyth (Offaly).