Ukraine club Shakhtar, winners of the final edition of the UEFA Cup last season before the competition was re-branded, were gifted the lead with a Marko Lomic own goal before cruising to victory with Luiz Adriano, Jadson and Yaroslav Rakitskiy all on the scoresheet as they moved to six points from two games.
Shakhtar also won their opening match 4-1 against Club Bruges.
PSV Eindhoven replaced CFR Cluj at the top of Group K after beating the Romanians 1-0 with Otman Bakkal's early header but fellow Dutch heavyweights Ajax Amsterdam had to settle for 1-1 draw away at Anderlecht in Group A.
Valencia, one of three Spanish clubs in action on a night of 24 ties, beat Italians Genoa 3-2 in Group B but Villarreal lost 2-0 to Salzburg in Group G as the Austrians followed up their opening victory over Lazio.
Serie A Lazio won 4-0 at Levski Sofia.
Werder Bremen beat Athletic Bilbao in Group L, Aaron Hunt's volley paving the way for 3-1 victory for the Bundesliga side who were beaten by Shakhtar in last season's UEFA Cup final.
The only two English Premier League clubs to reach the group stage both recorded victories. Everton beat BATE Borisov 2-1 in Belarus to top Group I while Fulham top Group E after beating Swiss side FC Basel 1-0 in west London.
Simone Perrotta was on target for Roma as the Italians, more used to life in the Champions League, hit back from defeat against Basel in their opening match to beat CSKA Sofia 2-0.
Fans paid a minute's silence in memory of Brice Taton, the Toulouse fan who was beaten by Partizan fans on September 17 and died on Tuesday, as the French club drew 2-2 with Bruges.
Portuguese giants Benfica were beaten 1-0 by AEK Athens in the Greek capital while Sporting enjoyed their first victory over a German club in 16 attempts, beating Hertha Berlin 1-0 to sit top of Group D.
The top two teams in each of the 12 groups progress to the last 32.
