The defence was powerless to halt Morrison's advance, and after evading them he capped his solo run by coolly lifting the ball over Tottenham goalkeeper Hugo Lloris.
Morrison's solo goal provided one of the best moments of the Premier Leauge so far this season and completed a 3-0 victory at White Lane on Sunday.
Elsewhere, Jack Wilshere found his spark in the second half to recover a 1-1 draw for Arsenal at West Bromwich Albion, two days after being admonished by Arsenal manager Arsene Wenger for his apparent smoking.
Although Arsenal's 10-game winning run in all competitions ended, the London club heads into the two-week international break level on points with Liverpool but topping the table on goals scored.
Chelsea is two points behind after late goals from substitutes Eden Hazard and Willian clinched a 3-1 win at Norwich.
But the highlight of the day was Morrison's memorable moment in the 79th minute at Tottenham.
"That is a genius goal for me," West Ham manager Sam Allardyce said. "You'll struggle to see a better goal than that this season. Tottenham had conceded two goals before today, but he just headed directly to (Jan) Vertonghen and (Michael) Dawson, slipped them like they weren't there and he used his outstanding ability to dink the goalkeeper."
The goal marked the latest step on Morrison's road to redemption.
The 20-year-old midfielder was offloaded in 2010 by Manchester United after then-manager Alex Ferguson finally lost patience with the prodigious but unpredictable talent.
After failing to settle at West Ham, he was loaned out to Birmingham last season but appears to have grown up and is now thriving.
"The penny has dropped with him," Allardyce said. "It has dropped in lifestyle and attitude and his timekeeping, all of a sudden there is a belief that he doesn't want to do anything other than break into our first team."
The game was already won by the time Morrison scored.
Allardyce's ultra-defensive formation had seen West Ham struggle to threaten Tottenham's goal until Winston Reid stunned the home fans by scoring in the 66th minute. Reid's header was inadvertently blocked by teammate Kevin Nolan next to the line but he immediately sent the rebound into the net.
Then Ricardo Vaz Te fortuitously added another six minutes later, with the ball coming off his knee after goalkeeper Hugo Lloris blocked an initial shot.
It was only Tottenham's second loss of the season.
"It's a wake-up call that we have to react to," Tottenham manager Andre Villas-Boas said. "We have to bounce back."
Chelsea, which drew its last league match at Tottenham, was back collecting three points again after late goals from a pair of substitutes.
Oscar was the first of the three Chelsea midfielders to find the net at Carrow Road in the fourth minute.
After Anthony Pilkington headed Norwich level in the 68th, Chelsea manager Jose Mourinho brought on Hazard and Willian off the bench.
Chelsea's lead was restored in the 85th after Norwich conceded possession from its corner and the visitors launched a blistering counterattack. After Alex Tetty failed to clear the ball, Hazard took advantage and unleashed a shot that squirmed under goalkeeper John Ruddy.
Willian was on target in the 86th on his Premier League debut with a curling strike into the top corner.
"The team — not just the boys who came on — coped well with the pressure," Chelsea manager Jose Mourinho said. "And, without using totally the balance, we could gamble and risk a bit to try and bring something different to the game to see if Norwich could cope."
Arsenal is still the team to catch, despite the setback at West Brom when it struggled to match the attacking fluidity on show in recent weeks.
West Brom threatened to repeat its victory over Manchester United last weekend when Claudio Yacob headed them in front before half time.
But as Arsenal found its rhythm after the break, Tomas Rosicky set up Jack Wilshere to equalize from outside the area in the 63rd with his first league goal since November 2010.
"He had a difficult first half where he was fouled a lot but showed he has character and kept going," Arsenal manager Arsene Wenger said. "At least that (barren run) is done now."