Incidents inside Lyon's stadium — which hosts the final next season — followed earlier clashes between French and Turkish fans on the streets.
Elsewhere, Manchester United stayed on course to complete its full set of European trophies by drawing at Anderlecht 1-1 in their first-leg game.
Henrikh Mkhitaryan scored in the first half and the Belgian side levelled in the 86th to add intrigue to the return match at Old Trafford next Thursday.
Ajax captain Davy Klaassen scored twice in a 2-0 win over visiting Schalke, whose goalkeeper Ralf Faehrmann stopped a rout.
Celta Vigo beat Genk 3-2 after trailing early then scoring three first-half goals.
LYON 2, BESIKTAS 1
After a 9:50 p.m. (1950 GMT) kickoff in Lyon, Besiktas led at halftime through Ryan Babel's low shot in the 15th minute. Lyon waited until almost time to score twice in two minutes.
Both clubs will be fined by UEFA, which increased security measures at all Champions League and Europa League matches this week after Borussia Dortmund's team bus was targeted by a bomb attack on Tuesday.
The disorder in Lyon spread about 20 minutes before the scheduled kickoff. French fans spilled on to the field for their own safety as fireworks were set off and missiles thrown from an upper section of the stadium housing Besiktas supporters.
Lyon president Jean-Michel Aulas was among the officials on the pitch trying to restore calm.
Besiktas likely faces the heavier sanctions from UEFA, which can close sections of the Turkish champion's stadium at the return match in Istanbul next Thursday.
ANDERLECHT 1, MANCHESTER UNITED 1
United will be favored to advance at Old Trafford next week after controlling much of the game in Brussels.
Jose Mourinho's team withstood an early wave of Anderlecht attacks, which failed to land an effort on target, then struck a post in the 17th. Jesse Lingard's shot rebounded out when he was fastest to reach a bouncing loose ball after Zlatan Ibrahimovic's close-range shot was saved.
Ibrahimovic played his part in a sweeping move to give United the lead. His pass to the right wing found Antonio Valencia for a cross that was met by Marcus Rashford's volleyed shot. Anderlecht goalkeeper Martinez Rubin dived right to push the ball spinning away toward the byline and, from a tight angle, Mkhitaryan hit a rising shot into the net.
Mkhitaryan has scored in four straight away games in the Europa League, which shapes as United's best route back to the Champions League if it can reach and win the final in Stockholm on May 24.
Midfielder Paul Pogba missed a good chance for United minutes before Anderlecht made the second leg a different proposition.
In the 86th, Leander Dendoncker ran clear of two United defenders to power a header from near the penalty spot past goalkeeper Sergio Romero.
AJAX 2, SCHALKE 0
Ajax, the 1992 champion, could have taken a more decisive lead to Germany next week.
Davy Klaassen's 23rd-minute penalty and shot in the 52nd from Justin Kluivert's cross were a poor reward for their dominance at Amsterdam Arena.
Ajax brought 10 saves from Schalke 'keeper Ralf Faehrmann and twice were denied by the goal frame.
CELTA VIGO 3, GENK 2
Seeking to keep the trophy in Spain for a fourth straight year, and sixth time since 2010, Celta Vigo found a resilient opponent in Belgium champion Genk.
After trailing inside 10 minutes to a Jean-Paul Boetius goal, Celta seized the lead eight minutes later and was 3-1 up at halftime. Pione Sisto, Iago Aspas and John Guidetti got the goals.
But Genk got a valuable second away goal in the 67th from substitute Thomas Buffel.
Genk, playing its 17th game in the competition it began in the second qualifying round in July, is unbeaten at home so far.
