Galway went on a scoring spree at Pearse Stadium as they picked up their first championship win under Henry Shefflin.
The Tribesmen cut loose in the opening half when they had the wind and led by 2-25 to 0-08 at the break, with ten players finding the target at that stage in an awesome display of shooting.
There was no way back for Westmeath, who never gave up but were 26 points adrift at the end of the contest.
Galway had the game wrapped up by the 13th minute when Cianan Fahy punished some sloppy defending to shoot to the net and push Galway 1-08 to 0-01 in front as they made the most of the wind.
Ten players hit the target for Galway in the opening half as they built up a 2-25 to 0-08 interval lead. Killian Doyle shot seven points for Westmeath, six of them frees and one from a '65, while former Galway player Davy Glennon got their only point from play.
Both midfielders and all six forwards hit the target from play by the 16th minute, while wing-backs Padraic Mannion and Fintan Burke also hit the target from distance.
Westmeath, who pushed Kilkenny last weekend for long periods, just had no answer as Galway were clearly fired up after letting a winning hand slip against Wexford in their opening match.
They had two points on the board inside 50 seconds and that set the trend for opening half. They shot 2-20 from their first 23 shots before recording half a dozen wides before the interval.
Galway got their second goal with a quality move, with Darren Morrissey starting it at the back before David Burke hit a superb long crossfield ball which Brian Concannon slipped into the path of Joseph Cooney and he raced through to finish superbly after 18 minutes.
Westmeath rallied somewhat after the restart with Derek McNicholas getting in for a goal after 40 minutes, while Killian Doyle’s accuracy kept chipping away at the lead.
But Galway pulled away again and Conor Cooney blasted home a 56th-minute penalty after he was fouled by Robbie Grevoille, who was black-carded as the Tribesmen ran out easy winners.
Galway: Éanna Murphy; Jack Grealish, Daithí Burke, Darren Morrissey (0-01); Pádraic Mannion (0-02), Gearóid McInerney, Fintan Burke (0-01); David Burke (0-03), Cathal Mannion (0-04); Tom Monaghan (0-01), Conor Cooney (1-08, 1-00 pen, 5f), Joseph Cooney (1-05); Evan Niland (0-02), Cianan Fahy (1-04), Brian Concannon (0-02).
Subs: Tiernan Killeen for P Mannion (half-time) Kevin Cooney for Monaghan (52), Gavin Lee (0-02) for Niland (59), Éanna Burke (0-01) for C Cooney (63), Johnny Coen for Daithi Burke (71).
Westmeath: Conor Bracken; Conor Shaw, Tommy Doyle, Johnny Bermingham (0-01); Aaron Craig, Robbie Greville, Jack Galvin; Cormac Boyle, Kevin Regan (0-01); Davy Glennon (0-01), Derek McNicholas (1-00), Joey Boyle; Killian Doyle (0-14, 12f, 1 ’65), Niall O’Brien, Niall Mitchell.
Subs: Conor Kane for C Boyle, Owen McCabe for McNicholas (51), Alan Cox for T Doyle (52), Jack Gillen for (58), Shane McGovern for O’Brien (65).
Referee: Patrick Murphy (Carlow).