Goals from Conor Cooney and Rory Burke in the closing seven minutes polished off a second win in a row for Galway in the Leinster SHC at Pearse Stadium.
Offaly, having drawn with Dublin in their opening match, again battled gamely but they were chasing the tie when they trailed by three points at the break having played with the wind.
Galway shot 19 wides in front of the crowd of 6,557 and also failed to convert a string of goal chances, yet never looked in danger.
Galway, similar to their opening round win over Kilkenny, laid the foundation for victory in the opening half playing against the wind when they led by 0-13 to 0-10 at the break.
They would have been out of sight had Offaly goalkeeper Liam Hoare not producing excellent saves to twice deny Rory Burke and also Jason Rabbitte, while Aaron Niland flashed another good opportunity across the goal.
But with Conor Whelan sharp at full-forward, Galway built a lead into the wind. Whelan landed three points in the opening 12 minutes - he got another one before the break - with Offaly shooting three wides before Dan Bourke got them off the mark after seven minutes.
Galway led by 0-08 to 0-03 at the end of the opening quarter with their sharper touch and good distribution proving decisive. Both sides shot eight wides in the opening half as they tried to master the wind.
A good Offaly spell which included a couple of points from Conor Doyle reduced the margin but with Galway captain Darren Morrissey keeping a close eye on Adam Screeny, Johnny Kelly's men never looked like getting in for a goal in that opening half.
They got the gap down to 0-13 to 0-10 at the break thanks to an effort from Jack Clancy and a 65 from Screeney.
Galway pushed that lead out to 0-19 to 0-13 by the end of the third quarter but they continued with wayward shooting, recording 19 wides by the end of the match.
A goal from Oisin Kelly from a tight angle just after he came on gave Offaly hope as they cut the gap to three points after 55 minutes, but Galway responded with three points in succession to ease the pressure.
Conor Cooney, again impressing off the bench, fired home their opening goal after 63 minutes after neatly flicking a Padraic Mannion delivery past Ben Conneely.
And they wrapped up the win when Rabbitte set up Rory Burke and this time he drilled low to the net.
Galway: Darach Fahy; Darren Morrissey, Cillian Trayers, Ronan Glennon; Padraic Mannion (0-01), Daithí Burke (0-01, Gavin Lee (0-01); Cian Daniels, Cathal Mannion (0-04, 1f); Rory Burke (1-02), Darragh Neary (0-01), John Fleming; Jason Rabbitte (0-02), Conor Whelan (0-05), Aaron Niland (0-09, 7f).
Subs: Conor Cooney (1-0) for Niland (55), Tom Monaghan for Neary (58), Colm Molloy for Fleming (65), Kieran Hanrahan for Trayers (66), Shane Morgan for D Burke (66).
Offaly: Liam Hoare (0-01f); Patrick Taaffe, Ben Conneely, Sam Bourke; Ciaran Burke, Killian Sampson, Ter Guinan; Ross Ravenhill (0-01), Jack Clancy (0-01); Shane Rigney (0-02), Dan Bourke (0-01), Conor Doyle (0-02); Charlie Mitchell (0-01), Brian Duignan (0-01), Adam Screeney (0-08, 5f, 1 65).
Subs: Ruairi Kelly for S Burke (half-time), Ben Miller for Clancy (46), Oisin Kelly (1-00) for D Bourke (54), Eoghan Cahill for Doyle (66), Ciaran Cleary for Ravenhill (68).
Referee: Thomas Gleeson (Dublin).
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