Chelsea scored three early goals before surviving a second-half scare to advance to the semifinals of the Europa League on Thursday with a 4-3 home win over Slavia Prague, and Arsenal beat Napoli 1-0 to make the last four for the second straight year.
In the other second-legged quarterfinal games, Valencia won 5-1 on aggregate after defeating Villarreal 2-0, and Eintracht Frankfurt overturned a two-goal deficit from the first leg. The German team went through on away goals following a 2-0 home victory over Benfica and 4-4 overall.
Chelsea enjoyed a 4-1 lead at halftime before conceding two goals after the interval for a 5-3 aggregate win. The London club equaled Atletico Madrid's record run of 15 unbeaten games in the competition.
Chelsea plays Frankfurt in the semifinals, and Arsenal, which won 3-0 overall, meets Valencia.
For all four semifinalists, winning the Europa League would secure a route into the Champions League outside of their domestic leagues.
Arsenal and Chelsea are currently locked in a tight fight with Tottenham and Manchester United for the last two qualifying spots from the Premier League behind Liverpool and Manchester City.
Valencia is sixth in the Spanish league, three points behind Sevilla in fourth. Frankfurt is fourth in the Bundesliga.
Here's a look at Thursday's games:
HAZARD'S RARE START
With Eden Hazard in a rare Europa League start, Chelsea was flying from the start.
Maurizio Sarri made five changes to a 2-0 loss to Liverpool on Sunday but Hazard retained his place in a sign of the growing importance of the competition for the manager.
After a 1-0 victory in the first leg in Prague a week ago, Chelsea doubled its overall lead five minutes into the game after Olivier Giroud freed Pedro to lob Slavia goalkeeper Ondrej Kolar. Five minutes later, Hazard crossed for an easy tap-in for Pedro across the goal but the ball bounced off the post to hit the head of Simon Deli before ending up in the net as an own-goal. In the 17th minute, Pedro and Giroud exchanged their roles for the France striker to make it 3-0 with his 10th goal in the competition to cement his top position in the scoring table.
Tomas Soucek pulled one back for Slavia with a header in the 26th, a minute before Pedro added his second on a rebound from close range.
Petr Sevcik netted twice for the visitors in a span of four minutes early in the second half to put Chelsea under pressure but the London club didn't allow any drama.
It was down and then up for Arsenal in the first half.
It lost Aaron Ramsey to what appeared a hamstring injury shortly before Alexandre Lacazette unleashed an unstoppable long-distance drive from a free kick to find the top of the net in the 36th minute.
It was the 50th game for Unai Emery in charge of Arsenal since replacing Arsene Wenger as manager. Emery used almost the same lineup as the 2-0 first-leg victory at the Emirates Stadium, with Granit Xhaka returning to take the position of Mesut Ozil in the midfield.
The win kept alive Emery's bid to win the competition for the fourth time, after doing so with Sevilla in three straight years from 2014.
Frankfurt rebounded from two straight defeats, including the 4-2 loss at Benfica in the first leg.
Filip Kostic was on hand to put Frankfurt ahead in the first half after Mijat Gacinovic's attempt from 20 meters (yards) hit the post.
Sebastian Rode scored the winner that sent Eintracht through with a shot from the edge of the box in the second half.
Toni Lato volleyed home in the first half for Valencia in its all-Spanish quarterfinal against Villarreal, and captain Dani Parejo sealed it with a deflected free kick in the second half.
Valencia also got past Villarreal in the semifinals of the 2004 UEFA Cup, a competition it went on to win. Villarreal can now focus on its effort to avoid relegation from the Spanish league.