Wilson's penalty - awarded following Ashley Young's handball - got Eddie Howe's side off to a good start in first half stoppage time at St. James' Park, with the 30-year-old's header making it two after the break in front of the watching England manager Gareth Southgate.
Joelinton rolled home a third soon after and, with the Magpies cruising, Almirón's blistering run in front of goal continued with a terrific goal from distance - his seventh of a fine campaign so far, and his sixth in the last month.
The margin of victory could have been even greater, too, with Wilson and Jacob Murphy both striking the woodwork as Villa failed to lay a glove on United, who are now just two points shy of third-placed Tottenham Hotspur.
Sean Longstaff, starting his sixth consecutive game for an unchanged United, set the tone for the hosts early on, winning possession 25 yards from the Villa goal and laying it off to the in-form Almirón. The Paraguayan spotted Kieran Trippier on the overlap and his cross was dangerous, but Wilson couldn't steer his header on target.
Longstaff then tried his luck with a speculative effort while over by the right touchline, clipping it over goalkeeper Emiliano Martinez but past the post, while Joelinton tried his luck too, cutting inside and testing the Argentine stopper after latching on to Fabian Schär's terrific ball over the top.
But it was a largely frustrating half, punctuated by a host of stoppages, for Howe's side. Villa only created one opening - a fine run from Leon Bailey, culminating in a superb challenge from Dan Burn to deny Emiliano Buendia. After the visitors lost Martinez to injury, substitute goalkeeper Robin Olsen got down well to deny Almirón just before the ten minutes of added time began at the end of the first period.
But Villa were unable to see out the half unscathed, as just a few moments later they conceded a spot-kick. The ball was worked to Almirón on the right and his shot was charged down by Young, whose raised arm prevented the effort reaching Olsen's goal. There were no arguments from the men in claret and blue as Wilson stepped up to dispatch the penalty straight down the middle beyond the Swedish custodian.
Wilson had the ball in the net again later in added time after racing onto Joe Willock's pass and finishing but while the goal was correctly ruled out for offside, the Magpies' intensity and intent remained after the break. Ten minutes after the restart, Wilson was at it again, pouncing at the back post to nod home Trippier's cross after a well-worked corner routine.
And three minutes later, Newcastle put the game to bed. It was a rapid breakaway, led by Wilson and Willock, which ended in the former Bournemouth man seeing his low drive parried by Olsen but only as far as Joelinton, who tucked away the rebound at the Gallowgate End to make sure of the points.
It got even better for Newcastle, and deservedly so. With a quarter of the contest remaining, Almirón netted yet another goal of the month contender. Wilson turned provider this time, although his lay-off was eclipsed by his teammate's subsequent stunner, curled into the far corner from 25 yards.
Howe's men were relentless. Wilson could have had a hat-trick 15 minutes from time when his header from substitute Jacob Murphy's cross cannoned back off the crossbar and just a minute later, Murphy had a go himself, seeing his strike bounce back off the base of the upright with Olsen rooted to the spot.
Other half-chances came and went for Joelinton, the tireless Longstaff and replacement Chris Wood, but they would only have added extra gloss to an already hugely satisfying afternoon for those in black and white. The scoring ended at 4-0, with the eventual result somehow looking almost kind on Villa, who were completely and thoroughly dismantled by Howe's outstanding fourth-placed side.
