Not according to the bookies!
The result still leaves them in the bottom three and they stay at 1/4 with Sky Bet to be playing their football next season in the Sky Bet Championship.
They are level on points with Sunderland ahead of the latter's game against Arsenal on Sunday with Sam Allardyce's side 4/5 for the drop and Norwich currently 1/3.
The Gunners are 1/25 for a top-four berth despite Manchester City moving above them into third with the Citizens 1/8. Manchester United are 7/2 and were otherwise engaged in the FA Cup semi-final.
Leicester and Tottenham are still to play this weekend with the Foxes 4/9 for the title and Spurs 7/4. Arsenal can be backed at 150/1.
Norwich – 31 points
Watford (h)
Arsenal (a)
Manchester United (h)
Everton (a)
Sunderland – 30 points
Arsenal (h)
Stoke City (a)
Chelsea (h)
Watford (a)
Newcastle – 30 points
Crystal Palace (h)
Aston Villa (a)
Tottenham Hotspur (h)