Pierre-Emerick Aubameyang struck twice as Arsenal defeated Ukraine's Vorskla Poltava 4-2 in the Europa League on Thursday, while in-form Chelsea began their campaign with a 1-0 win away to PAOK in Greece.
Aubameyang has struggled to hit top gear in the Premier League so far with just one goal in five starts, but the Gabon striker opened the scoring in London after 32 minutes of the Group E encounter.
Danny Welbeck nodded in a second just after half-time and Aubameyang curled in the Gunners' third, with Mesut Ozil also on target before a lapse in concentration saw Vorskla hit back with two late goals.
"I think we played well in the first half and in the beginning of the second as well," Aubameyang told BT Sport.
"We have to improve and try to fight not to concede a goal like we did in the last minute."
Premier League leaders Chelsea made a winning start to their Group L campaign as Willian's seventh-minute effort was enough to see off PAOK at a hostile Toumba Stadium.
Eden Hazard was omitted from the Chelsea squad at his own request due to fatigue, but manager Maurizio Sarri fielded a strong side as the Blues extended their winning run to six games in all competitions.
"We were in control of the match for 90 minutes. We had a lot of opportunities. We missed them and so I'm very happy with the three points, very happy with the performance, but not very happy with the result," said Sarri.
"When it's time to kill the match, we have to kill the match."
Steven Gerrard's Rangers acquitted themselves well on their first appearance in the group stage of a European competition since the 2010-11 Champions League, as they came away with a 2-2 draw against Villarreal.
A disastrous start for the Glasgow side saw Carlos Bacca fire Villarreal ahead inside 60 seconds, but Scott Arfield turned home a cross from Daniel Candeias to level on 67 minutes.
Gerard Moreno put the hosts back in front almost immediately, only for Kyle Lafferty to again hit back for Rangers as Gerrard's men made a solid start in Group G.
Red Bulls collide
Leigh Griffiths hit a late winner for Celtic in a 1-0 home victory over Rosenborg, a team Brendan Rodgers' side knocked out in this season's Champions League qualifying rounds.
Salzburg triumphed in the clash of Red Bulls in the other Group B fixture as Fredrik Gulbrandsen scored a minute from time to give the Austrian club a 3-2 victory over RB Leipzig.
Marseille, last season's runners-up, slumped to a 2-1 home defeat by Eintracht Frankfurt in Group H as Luka Jovic grabbed an 89th-minute winner for the reigning German Cup champions.
Lucas Ocampos opened the scoring early for Marseille, who were playing behind closed doors at the Stade Velodrome after numerous crowd incidents last season.
But Lucas Torro levelled on 52 minutes for Eintracht before Jovic's late strike won it.
Dudelange, the first Luxembourg team to play in the Europa League group stage, made seven-time European champions AC Milan work hard for a 1-0 win in Group F.
Luxembourg's Grand Duke Henri and Grand Duchess Maria Teresa were in the crowd as Dudelange, who have a dozen non-professional players in their squad, succumbed to a deflected second-half goal by Gonzalo Higuain.
Record five-time winners Sevilla launched their Group J campaign with a 5-1 rout of Standard Liege, as Ever Banega and Wissam Ben Yedder both netted twice for the Spaniards.