The Belgium striker broke through 22 seconds after the restart to bag his sixth goal of the campaign, the quickest second-half goal in the Premier League this season.
Nathaniel Clyne's long pass was deflected on by Adam Lallana to the lurking Benteke, who tucked it away from inside the area with Sunderland's defence caught napping.
Liverpool, who beat high-flying Leicester City 1-0 on Saturday with another second-half goal from Benteke, have 30 points from 19 games but Juergen Klopp's side are behind Manchester United on goal difference.
Sunderland remained second from bottom on 12 points after five straight defeats, seven points adrift of safety.
"Three points, really hard work," was Klopp's immediate verdict. "It's not the best we can do, we know this, but we had to fight.
"Everyone wants to end the year positively, we can and Sunderland can't but we take those points, go home, sleep two times and on to the next game," he told the BBC.
Sunderland manager Sam Allardyce cursed Sunderland's bad luck.
"Such a lucky, lucky goal for Liverpool," he told Sky Sports.
"If they'd come out with some of the brilliance they've got from Coutinho or Lallana and beaten a couple of players and wrapped it in the top corner, then you have to hold your hands up," he added.
Goalkeeper Vito Mannone had produced several great saves in the first half including a stunning dive in the 26th minute to deflect a goalbound Roberto Firmino shot against the upright.
The Black Cats, with only three wins this season, also showed fighting spirit with Liverpool keeper Simon Mignolet forced to palm over a Jermain Defoe effort in the 16th.
They suffered a setback on the half hour, however, when England midfielder Jack Rodwell was injured and replaced by Duncan Watmore.
Liverpool also lost their limping captain Jordan Henderson midway through the second half.
Benteke could have made it 2-0 in stoppage time but, clear on goal, he shot straight at Mannone.
(Reporting by Alan Baldwin, editing by Ed Osmond)
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