The Cats had led by 3-8 to 1-5 at half-time, with goals from Conor Martin, Chris Bolger, and Richie Reid, Paddy Purcell’s goal having put Laois into an early lead.
In the second period Reid, Donnelly, and Seán Morrissey found the net for Kilkenny too. Alan Murphy finished with six points for Brian Cody’s side, while Charles Dwyer had three points for Laois.
With Laois having beaten Kildare last weekend, another victory for Kilkenny over the Lilywhites this Sunday will see them through to the knockout stages.
At Abbotstown, Pat Gilroy’s tenure as Dublin hurling manager got off to a winning start as Meath were beaten by 4-17 to 0-14.
Donal Burke and Fionn Ó Riain Broin found the net for the Dubs in the first half as they assembled a 2-11 to 0-7 advantage and they pushed on in the second half, with Cian McBride adding a third goal before Ó Riain Broin got his second and their fourth.
Meath had edged out Antrim by a point in the first game in the group, meaning Dublin will top the group with a win against the Glensmen in Parnell Park on Sunday.
In Group 1, Wexford were pushed all the way by Carlow at Hollymount before prevailing on a scoreline of 1-20 to 0-18.
Cathal Dunbar’s late goal was crucial for the Model County as it pushed them 1-15 to 0-15 ahead, Davy Fitzgerald’s side having led by 0-9 to 0-7 at half-time.
The Dolmen County, who beat Wicklow at the weekend, were level soon after the restart and it was a see-saw affair until Dunbar’s crucial strike, with Lee Chin adding a free after that to open up a four-point advantage.
Diarmuid Byrne did help to bring Carlow back to within two points, but points from Chin, Matt O’Hanlon, Conor McDonald, and Jack Guiney ensured that Wexford wouldn’t be denied.
In the O’Byrne Cup, two early Tadhg McEneaney goals were a cushion Louth never relinquished as they beat Kildare by 2-11 to 0-9 at Hawkfield.
The pair of strikes had the Wee County 2-3 to 0-1 ahead in the first half’s early stages and Louth, who lost to Longford at the weekend, led by 2-6 to 0-7 at half-time. Gerard McSorley, James Butler, Bevan Duffy, and William Woods helped to extend the lead in the second half as they ran out comfortable winners.
At Netwatch Cullen Park, there was never much between Carlow and their visitors Meath, who won by 0-9 to 0-7 after a late surge.
Donal Lenihan and Ben Brennan were among the scores as Meath led by 0-4 to 0-3 at half-time, but Carlow drew level through Daniel St Ledger early in the second half and hit the front on the three-quarter mark with a Diarmuid Walsh point, Graham Reilly having had a Meath goal disallowed in between.
However, Brennan (two) and Lenihan had the late scores to give Meath the win, meaning a second victory this weekend against Wicklow will send them through.