Meath 2-14 Laois 0-10
Meath overcame the 54th minute dismissal of goalkeeper Paddy O'Rourke to claim a ten-point replay win in Tullamore.
Joe Sheridan (2-2) and Graham Reilly (0-4) were Laois' tormentors in chief, as the Royals advanced to a mouth-watering Leinster SFC semi-final against Dublin next weekend.
Meath led by 2-5 to 0-6 at half-time, thanks to Sheridan's goals, with MJ Tierney and Donal Kingston keeping Laois in touch.
However, Laois failed to score from play on the restart, allowing Meath to coast home.
12,659 spectators watched a game which Laois failed to get to grips with, as Sheridan's two-goal salvo in the first half provided the catalyst for Meath to pull through.
O'Rourke's dismissal, following a straight red card, was referee Maurice Condon's only sending-off, but he issued nine yellow cards, including five for the Royals, in what was a hard-fought contest.
With the strong contributions of MJ Tierney (0-3), John O'Loughlin (0-2) and Padraig Clancy (0-2) as substitutes for Laois in last Sunday's drawn game, the trio were expected to make some impact in the replay.
O'Loughlin and Tierney were handed starting berths, with Clancy entering the fray at half-time - but between them, they could only muster four points this time around, with all of those scores arriving from the boot of Tierney - three from placed balls.
Laois replicated their opening move from the drawn encounter, with Darren Strong picking off the first score of the game inside the opening 30 seconds.
However, the O'Moore men suffered an early blow when Meath hit back with a sixth minute goal. Cian Ward outpaced Laois centre-back Cathal Ryan to put Sheridan through and he clinically palmed the ball to the net.
Both sides had to cope with injuries as the first half wore on, with Laois' former AFL star Colm Begley forced off with a hamstring injury in the ninth minute, and Meath midfielder Mark Ward exited in the 23rd minute after an ankle knock.
Indeed, O'Connor Park resembled a hospital ward in the second quarter, with Ward's Meath colleague Michael Burke exiting the field on a stretcher in the 26th minute.
Action was a rarity at this stage, as Burke hit the deck following an accidental collision with O'Loughlin.
Although Laois pegged two points back through Padraig McMahon and Donal Kingston, a second Sheridan goal, in the fourth minute of injury-time, edged his side into a 2-5 to 0-6 interval lead.
Meath looked solid as they pushed four points clear, helped by a brace of scores from Graham Reilly and Shane O'Rourke, and Sheridan swooped on a loose ball to rifle home and add some cushion to their advantage.
Meath showed great pace and vision on the restart as they used their dominance in the midfield sector to great effect.
Laois were punished on four occasions inside a five-minute spell, as Meath raced into a 2-9 to 0-6 lead. Half-back Caoimhin King was on the end of a move involving Cian Ward and Gary O'Brien, edging the Royals six points clear.
Graham Reilly followed up with two more points and a well-taken Sheridan score opened up a double scores lead by the 40th minute.
Laois were finding it tough going, and a number of poor wides did little for their confidence. A second Kingston free was the lone score for Laois in the third quarter as Meath continue to show the greater cutting edge in midfield and up front.
Paddy O'Rourke was then handed his marching orders by referee Condon, after lashing out at Laois captain Padraig McMahon, but despite the absence of their net minder, Meath had a relatively untroubled finish.
Failing to plunder a score from play, a frustrated Laois were curtailed to four points from placed balls in the closing 35 minutes, as Meath deservedly won through to Leinster's last-four.
Next Sunday's Leinster SFC semi-final double header at Croke Park will see Meath take on defending champions Dublin at 4pm, with Louth and Westmeath battling it out in the second game (throw-in 5.50pm).
MEATH: P O'Rourke; C O'Connor, K Reilly, E Harrington; A Moyles, M Burke, C King (0-1); B Meade (0-1), M Ward; S Bray, G Reilly (0-4), S Kenny; J Sheridan (2-2), C Ward (0-3, 0-1f, 0-1 '45'), S O'Rourke (0-3).
Subs used: C Gillespie for M Ward (23 mins), O Lewis for Burke (26), G O'Brien for Moyles (half-time), B Murphy for Bray (54), C McGuinness for Kenny (66).
LAOIS: M Nolan; P O'Leary (0-1, 0-1 '45'), M Timmons, P McMahon (0-1); C Healy (0-1), C Ryan, C Begley; B Quigley, K Meaney; J O'Loughlin, D Strong (0-1), C Rogers; MJ Tierney (0-4, 0-3f), D Kingston (0-2, 0-2f), R Munnelly.
Subs used: D Booth for Begley (10 mins), B Sheehan for Ryan (34), P Clancy for Strong (half-time), P Lawlor for Rogers (50), D Rooney for Quigley (68).
Referee: Maurice Condon (Waterford)