Christian Fuchs scored twice to hand Dutchman Stevens a winning start to his second spell in charge in Gelsenkirchen having been appointed on Tuesday following Ralf Rangnick's resignation due to exhaustion.
"That was a good performance by us against a strong team. Haifa were technically accomplished and had quick movement," Stevens, whose side reached the Champions League semi-finals last term, told reporters.
Spanish compatriots Atletico Madrid, who lifted the trophy in 2010, grabbed a late 1-1 draw at Stade Rennes through Juanfran after Victor Montano's 30-metre shot took a wicked deflection to fly in on 56 minutes.
Atletico beat Celtic in their first outing with Radamel Falcao following up his heroics for last season's winners Porto with a goal for his new club but he failed to shine in Brittany.
Ki Sung-yong's penalty handed hosts Celtic an early lead but Udinese's Almen Abdi hit back also from the spot on 88 minutes for a 1-1 draw to leave the four-team Group I wide open.
Group D pacesetters Sporting beat Lazio 2-1 at home after scoring either side of Miroslav Klose's 40th-minute strike.
Also in Portugal, last season's runners-up Braga fell to a 2-1 defeat by in-form Club Bruges on a balmy evening.
Andy Johnson's brace gave fellow English club and 2010 runners-up Fulham a 2-0 win at Denmark's Odense after his 36th-minute shot went under the body of goalkeeper Stefan Wessels.
