The Belgium international endured a tough start to life at Anfield following a £32.5 million move from Aston Villa, with manager Jurgen Klopp claiming he was not fulfilling his potential.
Nevertheless, the 25-year-old has now made a telling contribution in back-to-back games with his 46th-minute effort at the Stadium of Light.
Benteke's goal took his tally in the Premier League to six this season and the striker was thrilled to be finding his range, having also scored the winner in Boxing Day's 1-0 win over Leicester City.
"I came to Liverpool to try to score lots of goals," he told Sky Sports after the match. "I'm in good shape and hopefully I can keep it up.
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"As a striker, when you start you have to score and help your team-mates. That's what I tried to do tonight and we won and we can be happy."
Starting at the Stadium of Light, Benteke put away his chance after Adam Lallana deflected a pass into his path.
The midfielder said there was an element of luck to his intervention, but was pleased to come away with a win as Jurgen Klopp's men moved up to seventh in the table, level on points with Manchester United.
"I don't think I meant it to go directly into Christian's path, but sometimes you need the rub of the green, especially when you come to a tough place like this where they're scrapping for every point," Lallana said.
"It could've been two or three at the end, on the counter we had our chances, but it's a great result for us.
"Hopefully we can push on and get another win Saturday [against West Ham]."