Powerful Purcell tore through Meath’s defence in the first-half and helped himself to 3-5, going on to claim 3-6 in total.
It wasn’t looking so promising for Laois after 19 minutes as they remained deadlocked on 0-5 apiece.
The visitors had also lost talisman defender Cahir Healy to an early hamstring injury but Purcell stepped up to the plate with a remarkable three-goal blast before the break.
“The guys are great to work with and we don’t individualise players but if one man should be individualised it’s Paddy Purcell,” said Kelly.
“It’s probably as good a midfield display as I’ve seen in a long, long time, if ever. It was phenomenal. He’s the ultimate professional.”
Meath’s midfield will have nightmares about the tie because Laois’ other midfielder Ross King scored 11 points.
Free-taker King converted seven placed balls as the Laois midfield scored a staggering 3-17 between them.
The result has left Laois sitting pretty at the head of affairs and eyeing a quarter-final clash with Wexford of Offaly.
They wrap up their group campaign against Kerry, whom Kelly managed to a Christy Ring Cup title in 2015, on May 14. That’s the same day that Meath travel to Westmeath knowing that, depending on results, they could either qualify for the quarter-finals or be relegated back to the Ring Cup.
Meath’s bad day was capped by Keith Keoghan’s 57th minute red card for a second booking.
Purcell’s second goal was the pick of the bunch as he flicked the ball out of a group of players, dinked it over a Meath defender and raced clear for a brilliant solo goal. His other strikes, in the 21st and 35th minutes, were laid on by Neil Foyle.
Laois led 3-13 to 0-7 at half-time and could afford to leak second-half Meath goals to sub Neil Heffernan and Joey Keena.
Laois finished strong with six points in a row to win at their leisure.
P Purcell (3-6); R King (0-11, 6 frees, 1 ‘65); N Foyle, A Corby (0-2 each); S Downey, B Conroy, W Dunphy, A Dunphy (0-1 each).
S Clynch (0-6, 4 frees, 1 ‘65); N Heffernan (1-1); J Keena (1-0); S Quigley, M O’Sullivan, A Forde, K Keoghan, A Gannon, S Brennan (0-1 each).
E Rowland; L Bergin, C Healy, D Palmer; M Whelan, C Collier, L Cleere; R King (c), P Purcell; S Downey, C Dwyer, S Maher; W Dunphy, P Whelan, N Foyle.
B Conroy for Healy (14); A Dunphy for Whelan (48); A Corby for Foyle (60); E Killeen for Dwyer (63); S Bergin for Maher (67).
S McGann; S Whitty, S Brennan, C Reilly; S Geraghty, K Keoghan, D Kelly; A Forde, J Keena; S Quigley, S Clynch (c), J Kelly; G McGowan, M O’Sullivan, A Gannon.
N Heffernan for Quigley (h/t); K Keena for McGowan (h/t); C McCabe for Kelly (48); P Farrell for Clynch (60); D Reilly for O’Sullivan (65).
J Keenan (Wicklow).