It was another game of missed chances for the Magpies, but the three points were vital, and Norwich's defeat was Steve McClaren's gain.
Leicester moved five points clear at the top of the Barclays Premier League after an impressive 3-1 win at title rivals Manchester City.
The Foxes took an early lead when defender Robert Huth flicked in a free-kick at the near post after just three minutes.
Leicester struck again soon after the restart when Riyad Mahrez produced a fine finish following a swift counter to make it 2-0 on 48 minutes, before Huth headed in a third from a corner on the hour.
City striker Sergio Aguero netted a late consolation on 87 minutes, but it was too little too late as Manuel Pellegrini's men fell further off the pace after Tottenham later moved up into second with a 1-0 win over Watford at White Hart Lane.
Spurs finally broke down a stubborn Hornets defence on 64 minutes when substitute Dele Alli, who had just come on, crossed through the six-yard box for Kieran Trippier to net from close range.
Liverpool 2 - 2 S'land
A Villa 2 - 0 Norwich
Man City 1 - 3 Leicester
Newcastle 1 - 0 W Brom
Stoke 0 - 3 Everton
So'ton 1 - 0 West Ham
Tottenham 1 - 0 Watford
Swansea 1 - 1 C Palace
Barclays Prem Results
Mauricio Pochettino's side have now won six straight matches in all competitions, edging a point ahead of City and two clear of north-London rivals Arsenal, who play at Bournemouth on Sunday.
Bottom club Aston Villa beat struggling Norwich 2-0, but remain some eight points adrift of safety.
Villa took the lead just moments before the break through Joleon Lescott's back-post header.
The home side doubled their lead when Gabriel Agbonlahor scored a first league goal for 11 months on 51 minutes.
Despite some late pressure, that proved enough to earn Villa a third league win and saw the Canaries slump into the relegation zone on the back of a fifth-straight league defeat.
Jermain Defoe scored a dramatic 89th-minute equaliser to secure relegation-battlers Sunderland a 2-2 draw with Liverpool at Anfield.
Reds manager Jurgen Klopp was not at the match after suffering a suspected bout of appendicitis, and - following a tepid first half - Roberto Firmino put the home side in front on 59 minutes.
The Brazil forward then turned provider for Adam Lallana to score a second with 20 minutes left.
In a protest against ticket prices, a significant number of Liverpool supporters left their seats during the 77th minute, demonstrating over-the-top priced admission of some £77 seats in the new main stand at Anfield.
With eight minutes left, Adam Johnson's free-kick squirmed past goalkeeper Simon Mignolet and there was still time for Defoe to complete a remarkable turnaround which saw thousands more home fans head swiftly for the exits.
1 Leicester 53
2 Tottenham 48
3 Man City 47
4 Arsenal 45
5 Man Utd 40
6 West Ham 39
7 So'ton 37
8 Everton 35
9 Liverpool 35
10 Watford 33
11 Stoke 33
12 C Palace 32
13 Chelsea 29
14 W Brom 29
15 B'mouth 28
16 Swansea 27
17 Newcastle 24
18 Norwich 23
19 S'land 20
20 A Villa 16
Everton collected their second victory of the week when they won 3-0 at Stoke.
The Toffees went ahead on 12 minutes through a penalty from Romelu Lukaku, while full-back Seamus Coleman headed in a corner to double the away side's lead on 28 minutes.
Winger Aaron Lennon scored for a third consecutive game to make it 3-0 after 42 minutes, which put the match beyond Stoke before half-time.
Swansea and Crystal Palace drew 1-1 at the Liberty Stadium in what was a first home game in charge for new boss Francesco Guidolin.
Gylfi Sigurdsson curled in a free-kick to put the Swans ahead on 14 minutes.
Palace levelled a minute into the second half when defender Scott Dann netted.
In the Saturday Night Football clash, Southampton held on to an early goal from Maya Yoshida to edge out West Ham 1-0 despite Victor Wanyama's red card.
Saints had to play for the majority of the second half with 10 men after Wanyama's dismissal - his third of the season - for a tackle on Dimitri Payet.
But West Ham could not find a way past a Saints rearguard which has now kept five consecutive clean sheets, with goalkeeper Fraser Forster yet to concede in seven and a half hours since he returned from a long-term injury.