David Moyes’ side comfortably sit top of the table after three games, six points clear of second-placed Dinamo Zagreb, who were beaten 2-1 at Rapid Vienna.
The Hammers had the majority of the possession but barely threatened in the first half until Craig Dawson looped home a header from Aaron Cresswell’s cross on the stroke of half-time.
They took total control with two goals in the space of two minutes just before the hour mark.
Issa Diop headed in via the crossbar from another fine Cresswell delivery, while Jarrod Bowen cut in from the right and fired in shortly after, though goalkeeper Maarten Vandevoordt will be disappointed at not keeping the low drive out.
West Ham were rampant and Nikola Vlasic could have converted a quick-fire fourth, but his shot from the edge of the six-yard box was blocked.
Genk were left to rue Paul Onuachu’s big chance in the first half when he beat goalkeeper Alphonse Areola to a cross, but sent his header wide of an open net.
Hammers continue to impress in Europe
West Ham collected a hard-fought victory over Everton on Sunday and backed it up with another impressive showing in Europe, where they are gathering some real momentum.
They finished sixth in the Premier League last term to secure a berth in the competition and just one more victory will guarantee a route to the last 16.
They didn’t have it all their own way on Thursday night against a Genk side that were champions of Belgium in 2019, qualifying for the Champions League where they finished bottom of a group featuring Liverpool.
The visitors thought they made the perfect start on eight minutes when Theo Bongonda headed in from close range, but the effort was ruled out for offside in the build-up.
Rangy striker Onuachu, who netted 35 goals last season, signalled a warning sign of his aerial ability when he headed over on the stretch before nodding wide when Areola came steaming off his line, but got nowhere near the ball.
That was Genk’s most notable chance of the game and they were punished for not capitalising on it as their hosts showcased the difference in class.
Tomas Soucek, who played the full game despite undergoing plastic surgery to a facial injury suffered against the Toffees, saw a header pushed away by Vandevoordt.
Ben Johnson’s low cross was then miscued by Bowen in the centre of goal, eight yards out, before centre-backs Dawson and Diop scored from headers either side of the break.
The contest was effectively over on 58 minutes when Vandevoordt failed to keep out Bowen’s shot which was straight at him.
The lead allowed Moyes to bring off midfielder Declan Rice and Cresswell, handing a European debut to 19-year-old Daniel Chesters, before their meeting with London rivals Tottenham on Sunday (kick-off 14:00 BST).