Munnelly struck two minutes into injury-time to put Mick O'Dwyer's side in front for the first time in the quarter-final tie, and banish the Offaly men to next month's All-Ireland qualifiers.

The first half witnessed some of worst shooting the championship has seen this summer with Offaly posting eight wides by the 20th-minute, and Laois waiting 13 minutes to feature on the scoreboard.

Despite that Kevin Kilmurray's Offaly still led 1-05 to 0-02 by half-time, thanks to Mark Daly's tenth-minute goal.

Pascal Kelleghan and James Coughlan laid the groundwork, and Lucan Sarsfields' clubman Daly did well to outpace Colm Begley to fire right-footed to the Laois net.

Padraig Clancy replied with a point for the O'Moore county before James Coughlan, Colm Quinn, Niall McNamee, Neville Coughlan and Daly tallied up Offaly's 1-05.

Munnelly (free) notched Laois' second point before the interval, and O'Dwyer's charges had more joy on the restart.

Noel Garvan and youngster Donie Brennan (0-02) scored early to sandwich a Kelleghan effort for Offaly, and reduce the arrears.

Munnelly chipped in with another free to push Laois within three, and while Chris Conway and Brennan were short with placed balls, both Quinn and Kelleghan hit the woodwork with attempts at the other end.

Offaly were shaky in front. Laois were not much better, but following John Reynolds and Neville Coughlan overs for Offaly, a wave of scores from Munnelly (0-02), Kevin Fitzpatrick and Conway had the 2003 winners at just 0-10 to 1-08 down, heading into injury-time.

Niall McNamee screwed a poor free shot wide - what could have been the insurance point for Offaly. He paid a heavy price as seconds later, a Laois break, set up by substitute Brian 'Beano' McDonald, saw Munnelly gather in a short Stephen Kelly point attempt, and creep through to grab the crucial goal, beating Offaly goalkeeper Padraig Kelly with a rising drive.

Laois face the winners of Westmeath and Kildare in the Leinster semi-final, in three weeks' time.