Summer signings Benteke and Roberto Firmino were both making their first starts, but the Brazilian gave Liverpool an early scare when he collided with Lawrence Vigouroux after trying to round the Swindon goalkeeper in the second minute.
Firmino needed treatment on the sidelines but returned to the action soon after, although Liverpool were forced to replace Joe Allen with Joao Teixeira just 11 minutes later when the Welshman took a knock.
Liverpool’s new signings combined for the first time on 18 minutes when Firmino cut the ball back for Benteke, who saw his close-range effort saved by Vigouroux.
Moments later, Teixeira curled over the bar before Emre Can’s long-range strike was gathered comfortably by Vigouroux.
Firmino dragged a shot wide of the target five minutes prior to the interval before Lazar Markovic fired straight at Vigouroux as the half ended goalless.
But within two minutes of the restart the Reds were in front through Benteke’s first goal for the club.
The Belgian international chested down a deft flick from Teixeira before firing an acrobatic volley past Vigouroux and into the top left-hand corner.
Benteke then had the ball in the back of the net seven minutes later but the 24-year-old was flagged off-side after latching on to a Firmino pass.
Swindon managed to snare an equaliser shortly after the hour mark when Jonathan Obika found the corner of the net with a curled effort that evaded Adam Bogdan.
Anton Rodgers – son of Liverpool manager Brendan – went close to putting the home side in front when his free-kick from the edge of the area landed on the roof of the net.
Benteke then made way for youngster Sheyi Ojo and three minutes from time the teenager netted a late winner. He raced on to a ball over the top before unleashing a ferocious half-volley which trickled into the net after Vigouroux managed to get a hand to it.
Saturday’s 2-0 win in Helsinki