Papiss Cisse scored twice at Stamford Bridge to take his tally to 13 goals in 12 appearances for Newcastle, which now looks to be going head-to-head with Tottenham for a top-four place.
Tottenham won 4-1 at Bolton to stay ahead of Newcastle on goal difference and move to within a single point of third-place Arsenal, which occupies the last automatic qualifying spot for next season's Champions League.
Fourth place usually guarantees a place in the qualifying rounds, but Chelsea could yet take that berth as defending champion by winning this month's Champions League final against Bayern Munich.
That would leave the Premier League's fourth-place finisher with only a place in the second-tier Europa League as a reward.
"It's all to play for still," Tottenham manager Harry Redknapp said.
Newcastle was a 100-1 outsider for a top-four place at the start of the season, but seems to have eliminated Chelsea from contention and could now finish there for the first time since 2002-03.
Cisse's 19th-minute opener was a left-foot volley into the top corner, and his second goal in injury-time was even better.
There seemed to be little danger for Chelsea, which brushed aside Queens Park Rangers 6-1 on Sunday, when Cisse collected the ball about 25 yards from the goal line and to the left of goal. But the Senegal striker smashed the ball with the outside of his right boot to send it swerving wildly through the air, over diving goalkeeper Petr Cech and in at the far post.
It was Newcastle's first league win at Stamford Bridge since 1986.
Newcastle now hosts Premier League leader Manchester City on Sunday before winding up its season at Everton on May 13. Chelsea has the FA Cup final on Saturday before its final two Premier League games, away to Liverpool and at home against Blackburn.
After just one win in nine games, Tottenham has rehabilitated its attempt to finish in the top four with two straight wins.
"I thought we showed tremendous ability on the break and finished them off with pace and goals," Redknapp said. "We've got a great chance and we're playing well.
Luka Modric put Spurs ahead in the first half with a spectacular half volley and, although Nigel Reo-Coker equalized in the 51st, Tottenham retaliated with three goals in 10 minutes.
Rafael van der Vaart restored the lead in the 60th and Emmanuel Adebayor made it 3-1 two minutes later with a far-post finish from Aaron Lennon's cross before completing the scoring from a pass through the middle.
It was only Tottenham's second Premier League win at Bolton and its first since 1996.
Bolton midfielder Fabrice Muamba greeted fans and watched Wednesday's game from the stands, less than seven weeks after his on-field cardiac arrest against Spurs in the FA Cup.
Muamba wiped tears from his eyes as he waved to supporters from the field before taking his seat to support his side.
"This is a special place: the support has been overwhelming and I am just grateful for that," Muamba said. "I am OK. I am getting stronger every day. I am happy to be back I am just happy to be able to speak to people again and walk freely."