Galway were pushed all the way by a resilient Laois side but the Tribesmen's greater class told in tonight's qualifier clash at O'Moore Park.
Eugene Cloonan, Damien Hayes and Iarla Tannian scored 2-14 between them as Ger Loughnane chalked up his first Championship win with the westerners.
Laois goalkeeper Patrick Mullaney landed two long range frees before Niall Healy (seven minutes) and Hayes (10) found the midlanders' net.
Four unanswered points from goalscorer James Young had Laois leading by 1-10 to 2-06 at half-time. But Cloonan helped Galway go back in front in the 49th minute and they never looked back.
Laois began the game in impressive fashion and settled early. Inside four-and-a-half minutes, Mullaney had launched over two memorable frees from inside his own 45-metre line.
Galway were level though, two minutes later, thanks to two Eugene Cloonan frees and although Niall Healy goaled in the seventh minute with a rasping shot and Damien Hayes also found the net three minutes later, the Tribesmen were unable to shake off a determined Laois challenge.
Damien Fox's hosts battled bravely and points from Tommy Fitzgerald and Joe Fitzpatrick (0-02) cut the gap before James Young blasted through a crowded goalmouth from a 21-yard free to leave just two points between the sides in the 21st minute.
Laois were strongest before the interval with four unanswered points from Young, including three from placed balls, ensuring a 1-10 to 2-06 interval advantage for Fox's industrious side.
Laois began the second half well with a pointed free from Young inside the opening minute and the midlanders continued to match the visitors well.
But once Galway broke in front in the 49th minute, following a fifth point from Cloonan, the Tribesmen strolled to victory.
It was the free-taking abilities of Cloonan along with good work from defender Ger Mahon which paved the way for the Galway victory.
Although Galway found the back of the Laois net for a third time thanks to a second Damien Hayes goal in the 64th minute, which put ten points between the sides, Laois fought on and were unlucky not to get a goal near the end after Young had a penalty well saved by Galway's debutant goalkeeper Colm Callanan.
GALWAY: C Callanan; D Joyce, D Cloonan, D Collins (capt); D Hardiman, J Lee, G Mahon (0-02); E Lynch (0-01), D Tierney; A Kerins (0-02), D Forde, I Tannian (0-03); N Healy (1-00), E Cloonan (0-10, 0-06f), D Hayes (2-01).
Subs used: R Murray for Lynch (half-time), K Broderick (0-01) for Healy (43 mins), K Wade for Cloonan (67).
LAOIS: P Mullaney (0-02, 0-02f); C Fitzpatrick, C Healy, C Dunne; Joe Phelan, M Whelan, M McEvoy; J Fitzpatrick (capt) (0-03), S Dollard; J Brophy, J Young (1-08, 1-07f), JJ McHugh; T Fitzgerald (0-01), W Hyland, P Russell.
Subs used: D McGill for Fitzpatrick (19 mins), B McEvoy for Phelan (48), D Bergin for Russell (62), C Delaney for Hyland (67), B Fitzgerald for McGill (68).
Referee: Dominic Connolly (Kilkenny).