Crystal Palace eased their growing worries as a 3-0 victory at home to Southampton ended a six-match losing streak.
They benefited from a comic opening goal as Fraser Forster, in front of new England manager Gareth Southgate, miskicked Jose Fonte's backpass to present Benteke with an absolute gift on his 26th birthday.
James Tomkins doubled their lead when he fired home from Andros Townsend's cross in the 36th minute and Benteke scored his second five minutes from time.
Sunderland registered only their third win of the season to move off the bottom of the table after a 2-1 victory at home to Leicester.
They went ahead thanks to Robert Huth's 64th-minute own goal after the Leicester defender diverted Jan Kirchhoff's header into the net and Jermain Defoe's instinctive strike, his eighth goal of the season, doubled their advantage.
Shinji Okazaki 's 80th-minute goal created a nervy finish for the home side, but they managed to hold on.
Swansea replaced the Black Cats at the foot of the Premier League after a 5-0 humbling at Tottenham, where a Harry Kane double took his tally to eight goals in as many appearances.
Spurs fortuitously went ahead when Kyle Naughton was harshly adjudged to have fouled Dele Alli, allowing Kane to score from the spot, but there was no doubt about Son Hueng-min's acrobatic volley on the stroke of half-time.
Kane added his second four minutes after the break, with Christian Eriksen scoring twice in the final 20 minutes.
West Brom moved ahead of sixth-placed Manchester United by virtue of having scored more goals after a 3-1 win at home to Watford.
Jonny Evans powered home a header from a corner by Chris Brunt, whose low free-kick took a deflection off Juan Zuniga to give the Baggies a comfortable half-time lead.
Christian Kabasele pulled one back on the hour from a corner, but Roberto Pereyra's red card for violent conduct ended their challenge, with Matt Phillips extending the hosts' lead in added time.
Burnley slipped to their third successive defeat as Stoke cruised to a 2-0 win at home.
Jon Walters swept in Mame Biram Diouf's cross for his first goal since March before Marc Muniesa started a move inside his own half before getting on the end of Marko Arnautovic's cross for his maiden Premier League goal in the 35th minute.