Ayoze Perez set Premier League Newcastle on their way into the FA Cup fourth round as they launched a first-half blitz to see off battling Luton 3-1.
Perez struck twice from close range before Jonjo Shelvey helped himself to a third inside nine minutes to send the Magpies in at the break in compete control.
The League Two leaders launched a concerted second-half fightback after Danny Hylton had replied four minutes into the second half and then seen a second ruled out for offside, before substitute Elliot Lee rattled the crossbar with a curling free-kick.
But despite the impressive onslaught, Rafael Benitez's men saw the game through to complete a more than satisfactory festive programme.
Keeper Freddie Woodman, making his first senior start for the club, was a little too relaxed when he allowed striker Hylton to get a partial block on his clearance as Luton worked hard to close down early on.
Woodman, an Under-20 World Cup winner with England, did not learn from his error and was almost made to pay three minutes later when Hylton repeated the feat only for team-mate James Collins to mis-control when the ball fell to him.
Jacob Murphy forced a diving save from Marek Stech with a curling efforts seconds later and Perez called on the Czech once again with a dipping 21st-minute effort on the turn.
But the keeper was at fault as the Magpies took the lead on the half-hour when he spilled Dwight Gayle's driven free-kick and Perez pounced to stab home amid the resulting scramble.
Stech was unfortunate to concede for a second time six minutes later when, after making a fine save to keep out Gayle's header, he saw Perez slide home once again to extend his side's lead.
The game was effectively over with six minutes of the first half remaining when Perez and Gayle combined to provide Shelvey with the simplest of opportunities to make it 3-0.
Midfielder Luke Berry headed over from a Lee corner in stoppage time and saw his shot after he had controlled half-time Harry Cornick's cross blocked by fellow substitute Isaac Hayden two minutes after the restart.
The visitors did reduce the deficit when Woodman's scuffed clearance was returned with interest and Hylton rounded the keeper and slotted home with the help of a deflection off covering defender Ciaran Clark.
Stech had to make a fine save from point-blank range to deny Perez his hat-trick with 50 minutes gone, but opposite number Woodman was relieved to see the offside flag go up as Hylton fired past him after latching on to a 57th-minute through-ball.
Newcastle had allowed their concentration to slip and handed Luton a foothold in a game which was becoming increasingly bad-tempered, and they might have been punished further when Lee crashed a 72nd-minute free-kick against the bar with Woodman rooted to the spot.
The Newcastle keeper had to parry Andrew Shinnie's dipping effort with 12 minutes remaining and as they wasted chances to kill off the tie, the Hatters remained in it until the final whistle.