Sky Bet make Norwich odds-on for the drop following their defeat to Fulham in Saturday's crunch game at the bottom of the Premier League.
Norwich could have opened an eight-point gap between themselves and Fulham with a win but instead went down 1-0 to a goal by Hugo Rodallega.
They are now just two points outside the relegation zone and with four tough fixtures remaining - they host Liverpool and Arsenal and must head to Manchester United and Chelsea - the bookies make them more likely than the Londoners to go down.
Norwich were cut to 4/9 for the drop, while Fulham's odds drifted to evens.
Cardiff also boosted their hopes of survival with a 1-0 win at Southampton - they are now three points from a position of safety. They were pushed out for relegation but at 2/7 are still very much expected to be playing Championship football next season.
Crystal Palace are now considered all but safe after a 1-0 win over Aston Villa - their relegation odds were moved out to 50/1.
Villa and West Brom, who blew a three-goal lead in their 3-3 draw with Spurs, will still have relegation fears but at 13/2 and 18/1 respectively, the layers expect them to survive.
In the top-four betting, Everton were trimmed again after moving into fourth for the first time in months.
A 1-0 win at Sunderland, who now looked doomed, saw them go two points clear of rivals Arsenal. Both sides have five games remaining.
Everton are now 11/10 but Arsenal, with the easier-looking fixture list, are 8/11.
The Gunners reached the FA Cup final on Saturday evening with a 4-2 win on penalties over Wigan and are Sky Bet's 1/4 favourites to lift the trophy.
Hull follow in the outright betting at 4/1 ahead of the second semi-final against Sheffield United, who are available at 16/1, on Sunday.
Premier League
11 West Ham 37
12 C Palace 37
13 Hull City 36
14 A Villa 34
15 Swansea 33
16 West Brom 33
17 Norwich 32
18 Fulham 30
19 Cardiff 29
20 Sunderland 25
Relegation run-in ...
SUNDERLAND (Pld 32 Pts 25 GD -25)
Apr 16 - Manchester City A
Apr 19 - Chelsea A
Apr 27 - Cardiff H
May 3 - Manchester United A
May 7 - West Brom H
May 11 - Swansea H
CARDIFF (Pld 34 Pts 29 GD -34)
Apr 19 - Stoke H
Apr 27 - Sunderland A
May 3 - Newcastle A
May 11 - Chelsea H
FULHAM (Pld 34 Pts 30 GD -40)
Apr 19 - Tottenham A
Apr 26 - Hull H
May 3 - Stoke A
May 11 - Crystal Palace H
NORWICH (Pld 34 Pts 32 GD -27)
Apr 20 - Liverpool H
Apr 26 - Manchester United A
May 4 - Chelsea A
May 11 - Arsenal H
WEST BROM (Pld 33 Pts 33 GD -11)
Apr 21 - Manchester City A
Apr 26 - West Ham H
May 4 - Arsenal A
May 7 - Sunderland A
May 11 - Stoke H
SWANSEA (Pld 33 Pts 33 GD -4)
Apr 13 - Chelsea H
Apr 19 - Newcastle A
Apr 26 - Aston Villa H
May 3 - Southampton H
May 11 - Sunderland A
ASTON VILLA (Pld 33 Pts 34 GD -14)
Apr 19 - Southampton H
Apr 26 - Swansea A
May 3 - Hull H
May 7 - Manchester City A
May 11 - Tottenham A
HULL (Pld 33 Pts 36 GD -6)
Apr 19 - Arsenal H
Apr 26 - Fulham A
May 3 - Aston Villa A
May 6 - Manchester United A
May 11 - Everton H
CRYSTAL PALACE (Pld 33 Pts 37 GD -15)
Apr 16 - Everton A
Apr 19 - West Ham A
Apr 27 - Manchester City H
May 5 - Liverpool H
May 11 - Fulham A
WEST HAM (Pld 33 Pts 37 GD -7)
Apr 15 - Arsenal A
Apr 19 - Crystal Palace H
Apr 26 - West Brom A
May 3 - Tottenham H
May 11 - Manchester City A