The £12million January signing struck with 58 minutes gone - his third goal in five games - to give the home side a precious lead, but it took a 70th-minute penalty saved by Karl Darlow to deny Magpies old boy Yohan Cabaye an equaliser.
Victory, coupled with Sunderland's draw at Stoke, eased Newcastle out of the bottom three ahead of Norwich's trip to Arsenal and left the bulk of a crowd of 52,107 dreaming of a great escape with just two games remaining.
Jermain Defoe scored an injury-time penalty to earn Sunderland a potentially priceless point at Stoke.
The Potters looked on course for victory after Marko Arnautovic gave them the lead five minutes into the second half but Defoe made it 1-1 having won the spot-kick himself.
1 Leicester 76
2 Tottenham 69
3 Arsenal 67
4 Man City 64
5 West Ham 59
6 Man Utd 59
7 Liverpool 55
8 So'ton 54
9 Stoke 48
10 Chelsea 47
11 Everton 44
12 Watford 44
13 W Brom 41
14 B'mouth 41
15 Swansea 40
16 C Palace 39
17 Newcastle 33
18 S'land 32
19 Norwich 31
20 A Villa 16
Newcastle's victory over Crystal Palace meant the draw was not enough to prevent Sunderland dropping back into the bottom three but it was more than they looked like getting for 90 minutes.
Arsenal celebrated in unison as Danny Welbeck's strike earned a 1-0 win which leaves Norwich's position ever more precarious.
The well-publicised protests in the 12th and 78th minute - to signal 12 years since Arsenal's last Premier League title - were a bit like the Gunners' season. Lots of expectation, poor execution.
And Welbeck gave Arsene Wenger reason for cheer and optimism of an 18th successive season in the Champions League with the decisive goal.
The Gunners' clash at Manchester City on May 8 will be crucial in determining their finishing position, while Norwich play at home to Manchester United the previous day desperate for points in their bid to avoid the drop.
West Ham sent out a European warning as they powered into fifth with an impressive win at West Brom.
Mark Noble's double and Cheikhou Kouyate's strike gave the Hammers a 3-0 victory which sent them above Manchester United on goal difference.
United will retake fifth spot if they avoid defeat against champions-elect Leicester on Sunday but the Hammers kept up the pressure and they have lost just once in their last 13 games in all competitions.
They face United in their final game at Upton Park on May 10 in what is set to become a winner-takes-all clash.
Left-back Leighton Baines' first goal since November 2014 secured Everton's first home league victory since early February but it was not enough to prevent growing opposition to Roberto Martinez's continued reign as manager.
A plane flying the banner 'Roberto must go' was followed by a handful of fans in the Gwladys Street End holding up 'Martinez Out' signs and chanting 'Get out of our club' at the end of the 2-1 win over Bournemouth.
Only five home league wins in the last 12 months tells its own story and it is unlikely Baines' goal, after Marc Pugh had cancelled out Tom Cleverley's strike inside the opening 10 minutes, will ease the pressure.
Troy Deeney grabbed two late goals to condemn Aston Villa to a club-record 11th straight defeat.
Deeney, a boyhood Birmingham fan, stuck the knife into the team he loves to score against more than any other as Watford ran out 3-2 winners.
Relegated Villa were leading with just five seconds of normal time remaining thanks to goals from Ciaran Clark and Jordan Ayew, either side of Almen Abdi's free-kick.
But the beleaguered midlanders, who had Aly Cissokho sent off with 15 minutes left, could not hold out as Deeney's double piled on the agony.
Premier League Relegation Run-Ins
NEWCASTLE (33pts)
Sat May 7 - Aston Villa A
Sun May 15 - Tottenham H
SUNDERLAND (32pts)
Sat May 7 - Chelsea H
Wed May 11 - Everton H
Sun May 15 - Watford A
NORWICH (31pts)
Sat May 7 - Manchester United H
Wed May 11 - Watford H
Sun May 15 - Everton A
Premier League Top Four Run-Ins
ARSENAL (67pts)
Sat May 7 - Manchester City A
Sun May 15 - Aston Villa H
MAN CITY (64pts)
Sun May 1 - Southampton A
Sat May 7 - Arsenal H
Sun May 15 - Swansea A
WEST HAM (59pts)
Sat May 7 - Swansea H
Tues May 10 - Manchester United H
Sun May 15 - Stoke A
MAN UTD (59pts)
Sun May 1 - Leicester H
Sat May 7 - Norwich A
Tues May 10 - West Ham A
Sun May 15 - Bournemouth H