After an even contest for the majority of the Premier League encounter, the game sprung into life in the closing stages as Everton midfielder Allan was sent off, after a lengthy VAR check, for a foul on United substitute Allan Saint-Maximin.
Following two long pauses in play, which included a protestor attaching himself to a goalpost, the Magpies agonisingly conceded in the ninth minute of stoppage-time through Iwobi's slotted finish, remaining nine points above the relegation zone.
Eddie Howe's side travelled to Merseyside bidding for a fourth consecutive victory over the Toffees, who were aiming to avoid a 12th Premier League game without a win.
United shot-stopper Martin Dúbravka was forced into action within the opening minutes as the Slovakia international held Ben Godfrey's header following Demarai Gray's dangerous corner.
Chris Wood, who netted his first Magpies goal against Southampton last week, went close to breaking the deadlock for the visitors after rising from Ryan Fraser's cross from the left flank but the Kiwi forward's header was comfortably saved by Everton goalkeeper Asmir Begović, replacing the ill Jordan Pickford.
Wood created another key opportunity in front of goal as the 30-year-old striker connected with Matt Targett's in-swinging corner but could only steer the ball over the crossbar.
Fabian Schär, captaining Newcastle for the evening, attempted a speculative free-kick from inside his own half but the Swiss defender's audacious effort was caught by the alert Begović.
The second-half barely began before play was halted for a number of minutes due to a protestor attaching himself to the goalpost, forcing stewards to free the male with bolt cutters after applying a cable tie around his neck.
Newcastle continued to push for a breakthrough as Emil Krafth tested Begović with a long-range volley after Dan Burn headed the ball into the Swede's path but the full-back's attempt was saved by the diving Begović.
Bruno Guimarães, who netted on his first United start against Southampton, went narrowly close to opening the scoring. After Miguel Almirón managed to advance past Godfrey down the right wing, the Paraguayan teed up the Brazilian midfielder, who saw his scuffed shot saved by Begović.
Dúbravka produced an important stop to prevent Anthony Gordon from breaking the deadlock as the Slovakian tipped the youngster's curling strike from the edge of the box over the crossbar.
Everton were then reduced to ten men as Allan received his marching orders from referee Craig Pawson. Saint-Maximin, introduced from the bench, began a dangerous run from inside his own half before the Frenchman was swiped down by the defensive midfielder.
After brandishing an initial yellow card, Pawson was forced to review his original decision, heading to the pitchside monitor before upgrading the booking to a red card.
Joe Willock was denied in the final minutes of normal time as the central midfielder fired a vicious low strike towards goal, forcing Begović to turn the ball out for a corner.
With 14 minutes of stoppage-time added on, Newcastle targeted a late winner as Saint-Maximin rose from Jacob Murphy's lofted cross from the right wing but could only direct his tame header into the side-netting.
In the 99th minute, United were dealt a devastating blow as Iwobi sent the hosts into the lead. After combining with Toffees substitute Dominic Calvert-Lewin, the former slipped a pass into the Nigerian's path, who fired a low first-time strike into the bottom right-hand corner.
