Both Manchester sides were made to work hard for their three points on Saturday, but three points they ended up with as City went clear of Arsenal at the top of the table with a laboured 1-0 win over Crystal Palace.
Manchester United were far from their attacking best at Carrow Road, but an astute substitution at halftime did the trick, as Danny Welbeck came off the bench to decide the contest with an opportunistic strike against Norwich to hand the Premier League side a 1-0 win.
Edin Dzeko, City's substitute extraordinaire, was the matchwinner for Manuel Pellegrini's men, finishing splendidly from 12 yards off a cross from Jesus Navas to end the stubborn resistance of Crystal Palace.
The three points takes City to the top of the table, two clear of Arsenal, who play Newcastle on Sunday. United also made their move up to sixth courtesy their victory over Norwich, with just seven points separating David Moyes' men from their crosstown rivals.
At Carrow Road, it was far from vintage Manchester United, as Norwich, desperate for three points, went at the reigning Premier League champions and were left wondering just how they did not go into halftime in the lead.
Despite much possession, United, with several changes to their side and without Wayne Rooney due to a recurrence of a groin strain, struggled for any kind of invention in front of goal, while Norwich were quite impressive going forward, with only their finishing letting them down.
Wes Hoolahan, in particular, had a couple of really goo thump-it-in-the-back-of-the-net chances go astray, as United rather held on towards the end of the first half.
Moyes made a change at halftime, bringing on the I-have-finally-shown-I-can-score-goals Welbeck for Ryan Giggs, with United starting the second 45 on the front foot - Shinji Kagawa and Ashley Young coming close early on.
Nathan Redmond, immediately after, at the other end fizzed a cross-shot wide as the end-to-end nature of the game refused to let up.
Moyes had an I-knew-it expression on 57 minutes as Welbeck, after a couple of lucky ricochets, sprang clear of the Norwich defence, before going around John Ruddy nicely to slot into an empty net.
The goal seemed to knock the stuffing out of Norwich and United saw off the final half an hour comfortably enough to pick up their fourth straight Premier League victory.
At the Etihad, it was not score-a-goal-every-ten-minutes-at-home Manchester City, as Tony Pulis' Crystal Palace, frustrated, hung on and nearly came away with an unlikely point, before Edin Dzeko put his right foot to good use on 66 minutes to give City a 1-0 victory.
The early game of the day between West Ham and West Brom, both in need of a win to get out of the we-don't-want-to-be-here relegation mire, served up a cracker, with six goals in all, three for each side.
West Ham opened the scoring via Joe Cole, who smashed in an effort at the near post after taking a neat pass from Kevin Nolan in just the fourth minute of the game.
The game, however, turned in West Brom's favour in the final five minutes before halftime, with Nicolas Anelka, yes him!, netting a quickfire brace.
The former Arsenal, Chelsea, Manchester City and Liverpool striker, first equalised, finishing astutely after taking a pass from Chris Brunt, before stabbing home from close range on the stroke of halftime.
West Ham were stunned by the quick reverse at halftime, but did not let the setback bother them as Modibo Maiga, in as a substitute for Carlton Cole, and Nolan scored in the space of two minutes to give the home side a 3-2 lead.
However, Saido Berahino would have the final say, twisting and turning inside the box before unleashing a powerful low left-footed drive to make it 3-3. Berahino would also shudder the post courtesy a brilliant freekick late in the game but a winner would not come for either side as they settled for a it-could-have-been-so-much-more point.
"I'm disappointed, I think we dominated the first half," Nolan told Sky Sports. "I've played with Nico [Anelka] before, he has quality all over, that's what he does. The manager [Sam Allardyce] was brilliant at halftime, he told us to calm down.
"That's the way our season has been going, quality goals scored against us. We have to stick together, it was another fantastic team performance. We deserved more today. I'm devastated we didn't get three points."
Results: Norwich 0-1 Manchester United, West Ham 3-3 West Brom; Manchester City 1-0 Crystal Palace; Hull 6-0 Fulham; Aston Villa 1-1 Swansea.