Danny Welbeck's late strike ensured a 1-0 win for Arsenal against Sporting Lisbon to extend their winning run to 11, while Ruben Loftus-Cheek scored a hat-trick as Chelsea won 3-1.
Danny Welbeck scored the only goal of the game as Arsenal beat Europa League rivals Sporting Lisbon 1-0 to extend their winning streak to 11 games.
After a largely forgettable opening half, the Gunners gradually improved after the interval and took control of Group E with the 1-0 victory at the Estadio Jose Alvalade.
Welbeck had already seen a header chalked off for a foul but he was on hand to steer home in the 77th minute to settle the contest in favour of Unai Emery's side.
The win means a draw in the return fixture at the Emirates Stadium in a fortnight could be enough to seal Arsenal's progression into the last-32 with two games remaining.
Ruben Loftus-Cheek fired a hat-trick for his first Chelsea goals in 30 months to seal the Blues' 3-1 Europa League win over BATE Borisov at Stamford Bridge.
England midfielder Loftus-Cheek is yet to start a Premier League match under new Chelsea boss Maurizio Sarri, but handed the taskmaster Italian an acute reminder of his talents with a coolly-taken treble.
Chelsea hardly had to shift into third gear to chug past their misfiring visitors and cement top spot in Group L, Aleksei Rios' late header scant consolation for the Belarusians.
Loftus-Cheek pressed his Premier League claims though, with his first Chelsea goals since finding the net in a 4-0 FA Cup win over Aston Villa on April 2, 2016.
The 22-year-old's six-minute brace had Chelsea two goals to the good just eight minutes in - and everything after that proved facile in the extreme.
Loftus-Cheek will care not on BATE's ineptitude however, and can rightly cite this free-scoring turn in future chats with manager Sarri over polite requests for more league action.
Celtic's Europa League hopes took another bruising in a 2-0 defeat by RB Leipzig at the Red Bull Arena.
A makeshift Hoops side shorn of several top stars made an encouraging start to the Group B match but were punished for defensive lapses, first on the half-hour mark by striker Matheus Cunha and again minutes later by attacker Bruma before the home side cruised their way through the second half.
Brendan Rodgers' men lost 3-1 to Salzburg in their previous European fixture and the Austrian side top the section with full points after their win over bottom side Rosenborg.
Celtic have three points from nine and host Leipzig, who have six points, next month but first face a crucial Betfred Cup semi-final against Hearts at Murrayfield on Sunday.
Meanwhile, Rangers surpassed Walter Smith's 1992/93 heroes to set a new record unbeaten run in Europe but were ultimately left frustrated as Spartak Moscow dug in for a 0-0 Europa League draw.
The Group G stalemate was the 11th game Steven Gerrard's side had managed without loss in continental action this term - beating the previous benchmark for a single season set by Smith's squad as they came within a whisker of reaching the inaugural Champions League final 25 years ago.
But the Ibrox boss will feel his team should have created more than a list of half-chances after dominating the crisis-hit Russians.
The draw allowed Villarreal to take over at the top of Group G but Gers remain very much in the hunt for the knock-out rounds with five points from their first three games.