West Ham began their Europa League campaign with a 2-0 win at Dinamo Zagreb in Group H while Celtic threw away a two-goal lead in a 4-3 defeat by Real Betis in Group G in the opening round of games on Thursday.
Red Star Belgrade, the 1991 European Cup winners, ground out a 2-1 home win over Portuguese rivals Braga while Bulgarians Ludogorets Razgrad earned a 1-1 draw at Danish side Midtjylland in Group F.
Michail Antonio gave West Ham a 22nd-minute lead in the Croatian capital when he rounded goalkeeper Dominik Livakovic and rolled the ball into an empty net after intercepting a poor back pass by Kevin Theophile-Catherine.
Declan Rice sealed the win with a fine individual effort in the 50th as he raced clear of his marker down the left from the halfway line and drilled the ball home through Livakovic’s legs from eight metres.
A stoppage-time goal from Paul Onuachu gave Belgians Genk a 1-0 win at Rapid Vienna in the other Group H match.
A bundled goal by Albian Ajeti and a Josip Juranovic penalty gave Celtic a 2-0 lead at Betis inside the opening 27 minutes but their joy was short-lived as the home side were level eight minutes later through Juan Miranda and Juanmi.
Betis rocked the visitors with another two quickfire goals shortly after the break, nosing ahead through Borja Iglesias in the 50th minute before Juanmi netted his second two minutes later after a slick move.
Anthony Ralston set up a tense finish when he pulled one back for Celtic in the 87th minute but Betis held on to come out on top in the seven-goal thriller.
In the other Group G game, Bayer Leverkusen fought back for a 2-1 home win against Ferencvaros as Exequiel Palacios and Florian Wirtz cancelled out an early Ryan Mmaee opener for the Hungarian side.
Left back Milan Rodic fired Red Star ahead in the 75th minute and Braga hit back through Wenderson a minute later only for Aleksandar Katai to delight the fervent home fans with an 85th-minute penalty.
In Group E, a Thomas Strakosha own goal midway through the second half helped Galatasray to a 1-0 home win over Lazio while 10-man Lokomotiv Moscow earned a last-gasp 1-1 home draw with Olympique Marseille.
Having had Nayair Tiknizyan sent off early in the second half, Lokomotiv fell behind to a Cengiz Under penalty before Faustino Anjorin salvaged a point for the Russian side with an 89th-minute goal.