The Newcastle boss received his marching orders, while Meyler was booked, in the 72nd minute following a tussle on the touchline.
Earlier, Tim Krul denied Alex Bruce with a fantastic double save and Newcastle went upfield and opened the scoring in the 10th minute via Moussa Sissoko from Mathieu Debuchy's pull-back.
Loic Remy doubled the score on 42 minutes after latching onto a poor back-pass from Maynor Figueroa and slotting into an empty net after rounding Allan McGregor.
Hull got back into the game soon after the interval when Curtis Davies headed home Tom Huddlestone's free-kick.
But Sissoko added his second on 55 minutes when slotting home the rebound after McGregor could only parry Yoan Gouffran's effort.
The game's main talking point arrived on 72 minutes when Hull midfielder Meyler barged into Pardew as he looked to retrieve the ball for a throw-in.
The Newcastle manager, no stranger to touchline altercations, squared up to Meyler before appearing to move his head in the direction of the Irishman. Referee Kevin Friend certainly viewed it as a serious incident and sent Pardew to the stands, with the FA sure to take a close look at the altercation in the coming days.
Vurnon Anita then tapped home a fourth goal in stoppage-time after Paul Dummett's cross to seal back-to-back wins for the Magpies following their victory over Aston Villa.
Newcastle started the brighter and Gouffran took aim with a strike from 20 yards that drew a dive from McGregor but was always drifting wide.
Huddlestone's free-kick then found Bruce at the back post but his header from point-blank range was somehow kept out by Krul, who then denied the Hull defender a second time.
And Hull's frustration was doubled within 30 seconds as Newcastle broke quickly, the ball eventually coming to Debuchy down the right whose low pull-back was met with a sweet first-time effort from Sissoko beyond the helpless McGregor.
Hull almost pulled level with 25 minutes gone, Ahmed Elmohamady's cross picking out Nikica Jelavic at the near post but his header went just wide.
The hosts very nearly had an equaliser in the 36th minute when Jelavic's free-kick deflected onto the crossbar.
Their first-half frustrations continued as Huddlestone's fine ball down the channel was collected by Shane Long, who twisted his man to create space before delivering a deep cross to the back post where Elmohamady headed wastefully wide.
And Hull's combination of ill-fortune and wastefulness in front of goal bit them again three minutes from the break when Figueroa inexplicably under-hit a pass-back which was seized upon by Remy, who rounded McGregor before slotting into an empty net.
Hull needed a speedy response at the start of the second half and that is exactly what they got as they immediately pulled one back. Huddlestone's free-kick was delivered into a crowd of players on the edge of the six-yard box, with Davies hanging in the air and nodding beyond Krul who got a fist to the ball but could not keep it out.
Yet Hull's hopes of a successful fightback were dashed on 55 minutes, a loose touch by Huddlestone in midfield inviting Sissoko to lead the breakaway. His pass picked out Gouffran who drilled a low shot that was only parried by McGregor, and it was Sissoko, smartly continuing his forward run, who lapped up the rebound.
Hull struggled to mount a response in what time remained and Newcastle saw Remy and Gouffran both go close to adding to the scoring before Anita added the gloss with a fourth in injury-time.
But the second half, and the match, were overshadowed by Pardew's ugly clash with Meyler which sadly will stand as the overriding memory of an otherwise thoroughly entertaining contest.