The stalemate at Stamford Bridge all but ended Chelsea's title bid, with Jose Mourinho's men now a point behind both leaders Manchester City and second-placed Liverpool with just one match of their league season remaining.
Liverpool will return to the summit if they win away to Crystal Palace on Monday.
However, City will still have a game in hand on both Liverpool and Chelsea after Monday's match at Selhurst Park.
Norwich's battling effort left them on 33 points with one game remaining and on the brink of relegation.
Sunderland are also in danger on 35 points but the north-east side have two games still to play as do West Bromwich Albion, who have 36 points.
Earlier, Arsenal celebrated their qualification for next season's Champions League with a 1-0 win at home to West Bromwich Albion on Sunday.
France striker Olivier Giroud scored the only goal of the game when he headed in a 14th-minute corner.
Everton's 3-2 defeat by Manchester City on Saturday meant Arsenal kicked-off at the Emirates Stadium knowing they could not be caught in the race for fourth place in the Premier League and a spot in next term's Champions League.
"I believe the mentality of the team was outstanding (in reaching the Champions League)," said Arsenal manager Arsene Wenger, whose side will look to end a nine-year spell without a major trophy when they face Hull in this month's FA Cup final at Wembley.
"We still have games in front of us
You can be pleased of the attitude, but frustrated because we were top of the league (for 128 days) then we dropped off."
The veteran French boss added: "We had injures -- three or four players who missed too many games
"And in some games, at the start away from home, we were caught by surprise
"We were perhaps too cautious and not confident enough
We paid a heavy price for it."
This result left West Brom three points above the relegation zone, but still with two games to play.
Although Sunderland and Norwich are still below his side in the table, Baggies manager Pepe Mel refused to accept the Midlands side had beaten the drop.
"No, an extra point we need, we have two matches and one point to get," he said.
"Now our only focus is on Sunderland
I think the players are very good professionals and every day and every week work on the pitch and there is a good atmosphere
I enjoy West Brom," the Spaniard added.
Source : AFP
Source: AFP