It was a rapid start from Eddie Howe's side at the King Power Stadium as Wood netted from the spot with two minutes on the clock, with winger Almirón making two five minutes later with a beautifully-worked goal to stun the hosts.
And Joelinton's bullet header effectively made sure of the points before the break as the Magpies gave their travelling supporters plenty of Christmas cheer, with the victory seeing United leapfrog reigning champions Manchester City to move into second spot behind leaders Arsenal.
It took just 90 seconds for Newcastle to pick up where they left off in the Premier League last month. Howe named the same side that had beaten Chelsea 1-0 in their final league outing before the international break, with Wood brought in for Callum Wilson in attack. It was the New Zealand international who hammered home the opener from the spot after Daniel Amartey's clumsy challenge on Joelinton inside the box handed United a belated Christmas gift, which Wood gratefully accepted.
And just five minutes later, it was two, and Howe's men were running riot. It was a terrific move from the visitors, which started inside their own half with an effortless pirouette from Bruno Guimarães. He clipped a pass out to Kieran Trippier on the right flank, who in turn lifted a pass down the line for Almirón to chase. The Paraguayan cut inside, played a one-two with the onrushing Guimarães before gliding through the Foxes' backline and slotting home his ninth goal of the season with ease.
The closest a disjointed Leicester got in the first period was a tentative poked effort from Patson Daka which was blocked by Nick Pope, and by the time the Magpies' third arrived just after the half hour it was threatening to become a rout. Trippier's corner from the right was met by Joelinton, whose thumping downward header extended their advantage and left their opponents - who had won four out of five in the league going into Monday's encounter - looking bereft of confidence.
Wood clipped a Joe Willock cutback just over before the break and though the hosts introduced Jamie Vardy for the second half, they posed few questions of United's defence. Sven Botman volleyed over as Newcastle looked for a fourth and while there wasn't quite the same intensity in the second 45, Howe's men were in no danger of surrendering their advantage.
After Dan Burn had inadvertently almost provided Leicester with a consolation after when a clearance struck him and drifted just wide, another Foxes substitute, Kelechi Iheanacho, let fly from distance, but his effort was far too high to trouble Pope. It took until the final eight minutes for Rodgers' side to muster an effort on goal and when they did - through Kiernan Dewsbury-Hall - it was tame.
Though Pope did have to hold onto a late Wilfred Ndidi effort and then get down to deny an offside Vardy, his clean sheet was never really in too much doubt as Newcastle ended a comfortable afternoon with a significant three points.
