The French striker hit the woodwork a number of times before the pair were both dismissed for a coming together late on, with the home side holding on for an important point.
The visitors' build-up to the game had been overshadowed by the imminent departure of Yohan Cabaye, who is poised to join Ligue 1 leader Paris Saint-Germain.
However, that appeared to be of little distraction to Alan Pardew's men who dominated proceedings without finding a way past Norwich goalkeeper John Ruddy.
Hatem Ben Arfa and Loic Remy provided most of the threat in the encounter, the latter hitting the woodwork in each half. Both teams finished the game with 10 men as Remy and Johnson were sent off following a melee in the final 10 minutes.
Norwich brought in Anthony Pilkington in place of on-loan winger Jonas Gutierrez, ineligible to play against his parent club. Meanwhile, Ben Arfa came in for the absent Cabaye and Sammy Ameobi taking the spot of the injured Yoan Gouffran in attack beside Remy, who threatened almost immediately, curling wide in the second minute.
Newcastle continued to dictate play and would have gone ahead 18 minutes in but for a fine save from Ruddy. The keeper did well to save a close-range Remy strike following a slick Newcastle move involving Ben Arfa and Moussa Sissoko.
Ruddy had to be alert again to prevent Sebastien Bassong from slicing into his own net soon after, before Johnson turned Remy's cross against his own post.
Luck continued to desert Pardew's men as their flurry of chances continued, Remy seeing a magnificent 24th-minute effort hit the post before Ruddy denied Ben Arfa with a strong stop.
Norwich did manage to gain something of a foothold in the game as the first period wore on, but should have been behind just before the break. However, Ben Arfa's lack of composure after Sammy Ameobi’s pull back to let the club off the hook.
The home side made a better start to the second half but Newcastle remained more dangerous in front of goal, Remy striking the crossbar with a free kick.
Ben Arfa went close with another set piece on 67 minutes, but the Frenchman was forced off less than 10 minutes later and replaced by Shola Ameobi.
Norwich created its first real chance of the game shortly after that switch, with Gary Hooper rattling the bar from close range.
It was an ill-tempered end to the game as Johnson and Remy each saw red for their part in a scuffle, meaning the QPR loanee will miss Newcastle's Tyne-Wear derby with Sunderland on Saturday.
Despite the club's dominance, the visitors had keeper Tim Krul to thank for preserving a point as he kept out Robert Snodgrass’ point-blank header with a superb reflex save.