First-half strikes from Said Benrahma and Jarrod Bowen put the hosts into a comfortable two-goal lead, and although Sebastiano Esposito pulled one back for the visitors late on from the penalty spot, the Hammers held on to maintain their perfect start in the group stage.
West Ham sit at the summit of Group B with a maximum of 12 points from four matches, six points clear of Silkeborg who have leapfrogged Anderlecht into second place following their emphatic 5-0 home win against FCSB.
David Moyes made eight changes to the side that beat Fulham in the Premier League last weekend, with Benrahma among those brought into the first XI.
Indeed, the Algeria international broke the deadlock for the Hammers in the 14th minute when he curled a free kick up and over the wall and into the bottom-left corner.
West Ham were then dealt an injury blow in the 23rd minute when centre-back Angelo Ogbonna gingerly walked off with an apparent knee problem - the 34-year-old was starting just his fifth game of the season after spending around nine months on the treatment table with a serious ACL injury.
The Hammers continued to dominate proceedings and they doubled their lead on the half-hour mark when Emerson Palmieri cut the ball back to Bowen just inside the penalty box, with the Englishman shifting the ball onto his favoured left foot before unleashing a powerful strike beyond Anderlecht goalkeeper Hendrik Van Crombrugge.
Bowen's goal has seen him become West Ham's joint-top record scorer in European competition with six strikes along with Johnny Byrne and David Cross.
Anderlecht responded with two chances of their own towards the end of the half from Belgian playmaker Yari Verschaeren and Italian striker Esposito, the former directing a side-footed strike narrowly wide before the latter watched his effort tipped behind by Alphonse Areola.
West Ham remained on top in the second 45 and were knocking on the door for a third goal, while Anderlecht struggled to escape their own half.
However, Moyes was dealt another injury blow in the centre-back department as Craig Dawson - who came on for Ogbonna in the first half - walked straight down the tunnel in the 75th minute after sustaining a knock, with his replacement Tomas Soucek slotting into the back three alongside fellow substitute Declan Rice and Emerson.
West Ham were in cruise control as they edged closer to full time, but Anderlecht were given a glimmer of hope in the 87th minute when the referee controversially pointed to the penalty spot after Ben Johnson was deemed to have caught Esposito inside the area.
The Inter Milan loanee stepped up and tucked away his effort from 12 yards, but the Belgian outfit were unable to find a late equaliser, with the Hammers holding on to book their place in the knockout rounds with two group games to spare.
West Ham will now turn their focus to Sunday's Premier League trip to St Mary's to face Southampton, with Moyes's men aiming to climb into the top half of the table.