Also, Joao Felix's hat trick guided Benfica to a 4-2 win over 10-man Eintracht Frankfurt, handing the Bundesliga side its first defeat in the Europa League this season. In an eastern Spain derby, Valencia secured a 3-1 away win at Villarreal after scoring a couple goals in injury time.
For Arsenal and Chelsea, winning the Europa League would secure a route back into the Champions League if they fail to finish in the top four in the Premier League. The two are currently locked in a tight battle with Tottenham and Manchester United for the last two qualifying spots behind Liverpool and Manchester City.
Napoli is second in Serie A and has no such worries but Valencia, currently sixth in the Spanish league faces the same scenario. The second legs will be played on April 18. Here's a look at Thursday's games:
ARSENAL EARLY ATTACK
Arsenal translated its dominant start into a two-goal advantage within just 25 minutes.
Ramsey finished a flowing Arsenal move to net the first in the 15th while Lucas Torreira doubled that advantage 10 minutes later with a shot deflected by Koulibaly for an own goal.
Ramsey had a great chance to add a third goal in the second half but blasted a shot over the bar from six yards out after being teed up by substitute Henrikh Mkhitaryan, while Pierre-Emerick Aubameyang and Ainsley Maitland-Niles also missed opportunities to increase the lead.
"We deserved a third goal," Arsenal manager Unai Emery said. "Away it is going to be different. We need to be focused and clear; no more confident than we need."
Mesut Ozil started for the sixth straight game for Arsenal after regaining the trust of Emery and was at the heart of most of the hosts attacks before being taken off for Mkhitaryan.
ALSONSO STRIKES LATE
Chelsea manager Maurizio Sarri rested seven players who started in a 2-0 win over West Ham on Monday, including Eden Hazard and Gonzalo Higuain, and his team struggled to create chances before finally finding a breakthrough in the 86th minute in Prague.
Only Willian managed to threaten Slavia's goal in the first half with a shot that bounced off the crossbar after Chelsea withstood Slavia's early pressure.
Sarri sent on Hazard in the 59th minute to spark his attack but Chelsea goalkeeper Kepa Arrizabalaga had to produce several saves before Marcos Alonso came to the visitors' rescue, heading in the winner from a pinpoint cross by Willian.
"The second leg will be difficult," Sarri said. "This opponent is very dangerous away. I'm very happy with the result."
The sections in the Eden Stadium used by Slavia's hardcore fans were empty due to a punishment by UEFA for fans throwing objects onto the field during a 0-0 draw with Genk in the first leg of the round of 32 on Feb. 14.
In a separate incident, three Chelsea supporters were refused entry to Thursday's game after being identified as part of the group in a video appearing to sing a racist song about Liverpool forward Mohamed Salah.
Sarri offered no comment after the game, saying he didn't see the video.
But Chelsea said it "finds all forms of discriminatory behavior abhorrent and where there is clear evidence of Chelsea season ticket holders or members involved in such behavior, we will take the strongest possible action against them."
FELIX ON TARGET
In-form Frankfurt's hopes of a good first-leg result in Lisbon were dashed in the 20th minute when defender Evan N'Dicka received a straight red card and Felix converted the resulting penalty.
Frankfurt, which is fourth in the Bundesliga standings, managed to answer five minutes before halftime through Luka Jovic, who is on loan from Benfica. But Felix restored Benfica's lead with a powerful low long-distance drive just three minutes later.
Ruben Dias headed home in the second half to stretch the lead before Felix completed his first hat trick for Benfica. Substitute Goncalo Paciencia pulled one back for Frankfurt to give the German side a better chance of overturning the deficit.
Benfica has never lost at home in any stage of the Europa League, with 19 wins and three draws.
VILLARREAL COLLAPSES LATE
Villarreal suffered yet another late collapse to give Valencia a firm grip of their all-Spanish quarterfinal, as Daniel Wass and Goncalo Guedes both scored for the visitors in injury time.
Valencia had taken the lead six minutes into the game despite captain Dani Parejo missing a penalty, as Guedes was on hand to score from the rebound.
Santi Cazorla made no mistake from the spot at the other end as he calmly equalized in the 36th for his second goal in the Europa League.
But Villarreal, which is 18th in the Spanish league, has made a habit of conceding late goals. It wasted a two-goal lead in a recent 3-2 loss at Celta Vigo in the league and then couldn't hold on to a 4-2 lead against Barcelona, conceding twice in injury time then as well for a 4-4 draw.
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