Vincent Kompany joined Anderlecht from Manchester City in 2019 as player-manager, and now takes over from Franky Vercauteren, who had been handling coaching duties, in a purely managerial role.
The scrappy, sapping victory means Jose Mourinho's Manchester United remain on course to claim the only major trophy missing from the club's collection.
Leander Dendoncker struck late to snatch a 1-1 draw for Anderlecht against Manchester United in the first leg of Thursday's Europa League quarter-final, while crowd trouble overshadowed Lyon's tie with Besiktas.
The Europa League quarterfinal clash will be the fourth meeting between Manchester United and Anderlecht, with the English club winning the three previous ones.
Arsenal were on course to qualify for the knockout stage of Europe's elite club competition for the 15th successive season, but the Gunners' creaky defence was brutally exposed by Anderlecht in a remarkable finale that saw the Belgians score three times in the last 29 minutes.
Cristiano Ronaldo hit his 70th Champions League goal -- one short of the all-time record 71 held by Raul -- as Real Madrid beat Liverpool 3-0. In Brussels, late goals by Kieran Gibbs and Lukas Podolski handed Arsenal a dramatic 2-1 win away to Anderlecht.
Ailing Russian champions Zenit St Petersburg grabbed their first win of this season's Champions League campaign here on Wednesday with an unconvincing 1-0 win over Belgian opponents Anderlecht.
AC Milan failed to shrug off their disappointing form as they were held to a 0-0 draw by Anderlecht at home in the Champions League football first round group match.
Serbian international winger Milan Jovanovic has left Liverpool for Anderlecht on a two-year deal, the Belgian club confirmed on Tuesday.