Johnny Heitinga's injury-time goal enabled Everton to overcome battling Bolton and book a place in the fifth round of the FA Cup.
Blackpool came from behind twice to force a 2-2 draw with Bolton and avoid defeat in their first match under new boss Michael Appleton.
Bolton have been relegated from the Premier League after being held to a draw by Stoke at the Britannia.
James Morrison came off the bench to score a last-minute equaliser as West Brom put a severe dent in Bolton's chances of avoiding relegation.
Tottenham won back-to-back league games for the first time since January as they reinvigorated their Champions League hopes by beating Bolton.
Kevin Davies scored twice to earn Bolton a valuable point as Sunderland failed to win for a sixth league game.
David Ngog completed a fine comeback win for struggling Bolton as Aston Villa's relegation fears increased.
Chris Eagles rescued a point for relegation-threatened Bolton, who were given a stern test by Swansea.
Hatem Ben Arfa's second-half wonder goal lightened up a dreary contest with Bolton and set Champions League chasing Newcastle on the way to a fifth successive victory.
Clint Dempsey's first-half double helped Fulham to a rare away success that ended relegation-threatened Bolton's three-game winning run.
Wolves capitulated after taking the lead to leave themselves in deep trouble at the bottom of the table.
Second-half goals from Ryan Nelsen, Gareth Bale and Louis Saha sent Tottenham into the semi-final of the FA Cup, where they will face Chelsea.
See English Premier League fixtures for the season 2013-2014.
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