Gunners and Blues miss out on Euro bids.
The Gunners hit the woodwork twice through Robin van Persie and Laurent Koscielny, and van Persie had other clear-cut chances, but could not get the better of Petr Cech.
Otherwise, Chelsea were arguably the better side, but were let down by their execution in the final third as they stayed sixth with just four games remaining.
Newcastle's Champions League hopes are on the rise as they claimed a convincing 3-0 victory over Stoke thanks to two goals from Yohan Cabaye.
Cabaye fired Newcastle in front after 14 minutes, knocking home the rebound after a Papiss Cisse header came back off the crossbar.
The Frenchman then turned provider four minutes later when he produced a slide-rule pass to put Cisse in on goal, and he made no mistake with a left-foot finish.
Newcastle's third arrived after 57 minutes with Cabaye again at the heart of things, firing Demba Ba's assist into the corner.
The win lifted the Magpies up to fourth spot above Tottenham, who missed the chance to return there as they fell to a 1-0 loss at QPR in the evening kick-off.
Adel Taarabt's 25th-minute goal fired Rangers three points clear of the relegation zone, although the former Spurs man was later sent off.
Blackburn's hopes of escaping the bottom three were given a welcome boost with a 2-0 win over Norwich at Ewood Park.
Ayegbeni Yakubu had hit the post for the home side after 38 minutes, but they were in front three minutes later with Morten Gamst Pedersen whipping in a cross for Mauro Formica to sidefoot home.
Junior Hoilett added another four minutes into the second half, curling a shot into the top corner.
The win was not enough to lift Blackburn out of the drop zone, but they climbed above Bolton who were held to a 1-1 draw by Swansea.
The Swans took just six minutes to break the deadlock through Scott Sinclair, who unleashed a superb shot into the top corner.
But Bolton were level after 14 minutes when Chris Eagles provided a left-footed finish to Martin Petrov's cross.
Wigan's survival hopes suffered a setback with a 2-1 defeat against Fulham at Craven Cottage.
The Latics were looking to claim their fifth win in six Premier League matches - a run which had carried them away from the relegation zone - and Emerson Boyce smashed home from the edge of the area to give them a 58th-minute lead.
But Fulham were level a minute later with Pavel Pogrebnyak driving home a low shot, and a header from Philippe Senderos a minute from time snatched the points for the Cottagers.
Aston Villa and Sunderland had to settle for a goalless draw at Villa Park.
* Robin van Persie tries a shot but is challenged by Chelsea's Gary Cahill