Barcelona stumbled to a goalless draw with Galatasaray in their Europa League last-16 first leg at the Camp Nou on Thursday, while Rangers cruised into a 3-0 lead in their tie against Red Star Belgrade.
Xavi Hernandez's Barca, playing in Europe's second-tier competition for the first time since 2004, dominated for long periods.
But it was their Turkish visitors who almost grabbed a lead ahead of the return game in Istanbul next week, with Bafetimbi Gomis only denied a winner by a VAR review for offside.
Memphis Depay, making his first start since December, forced Galatasaray goalkeeper Inaki Pena into two good first-half saves.
Jordi Alba, Ousmane Dembele and Frenkie de Jong all went close in the second period for Barcelona, but the hosts could not find a breakthrough.
Xavi's side are still unbeaten in 90 minutes since defeat by Bayern Munich in their final Champions League group game last year.
But the Catalan giants will likely have to find a victory next Thursday to extend their bid to win this competition for the first time.
There were goals galore in the third-tier Europa Conference League, with PSV Eindhoven and FC Copenhagen playing out a remarkable 4-4 draw.
The Danish visitors led 3-1 and 4-3 at the Philips Stadion, but Eran Zahavi grabbed an equaliser with five minutes remaining for PSV after Cody Gakpo had scored twice and missed a spot-kick.
Leicester saw off French side Rennes 2-0 at the King Power Stadium as Kelechi Iheanacho's injury-time effort added to Marc Albrighton's opener on the half-hour mark.
Jose Mourinho's Roma claimed a 1-0 win at Vitesse Arnhem and Marseille conceded a late goal in a 2-1 success against FC Basel at the Stade Velodrome.
Feyenoord romped to a 5-2 thrashing of Partizan Belgrade in Serbia in a bad night for the country's capital clubs, and Slavia Prague saw off LASK Linz 4-1.