Former European champions Liverpool and Juventus will take slender leads into the second legs of their Europa League playoffs after narrow victories Thursday. In unfamiliar territory after failing to qualify for the Champions League last season, fallen English giant Liverpool needed Ryan Babel's 45th-minute goal to edge past Trabzonspor 1-0 at home, while Amauri's injury-time strike earned Juventus a 2-1 first-leg victory at Sturm Graz. Russian side Sibir Novosibirsk caused the shock of the night by winning 1-0 at home to Dutch club PSV Eindhoven, which played all of the second half with 10 men following the sending-off of Francisco Rodriguez. Elsewhere, Borussia Dortmund thrashed Qarabag 4-0 and big-spending Manchester City beat Timisoara 1-0 through a goal on debut by new signing Mario Balotelli. The return legs are next week. Without captain and midfield heartbeat Steven Gerrard, Liverpool looked like it was going to push on for a convincing win at Anfield when Netherlands winger Babel, starting up front with Fernando Torres on the bench, collected a pass from Joe Cole and slipped a neat finish into the corner. But the five-time European champion failed to add a second, with summer signing Cole having a 52nd-minute penalty saved. Juventus took the lead in the 15th minute through Leonardo Bonucci but was pegged back with eight to go when Gordon Schildenfeld equalized for Graz. Brazilian striker Amauri was the match-winner when he struck in the first minute of stoppage time to give the visitors a cushion to take back to Turin. Aleksandr Degtyarev scored in the second minute of injury time as PSV was humbled by Sibir. The Dutch side was not helped by the red card shown to Rodriguez six minutes before halftime. Another surprise result in qualifying for Europe's second-tier club competition saw Portugal's Sporting Lisbon lose 2-0 at home to Brondby, Jan Kristiansen and Ousman Jallow scoring either side of the interval for the Danish side. Dortmund and fellow German sides Bayer Leverkusen and Stuttgart set themselves up well for their return legs with solid wins. Shinji Kagawa and Lucas Barrios each scored twice in the first half to guide Dortmund to a comfortable victory against the visitors from Azerbaijan. Michael Ballack converted an injury-time penalty after coming on as a substitute for his game since re-signing for Leverkusen, sealing a 3-0 win against Tavriya Simferopol. Michal Kadlec scored Leverkusen's other two goals. Substitute Martin Harnik was the match-winner for Stuttgart, scoring with two minutes left to secure his side a 1-0 victory at Slovan Bratislava. That match was interrupted for five minutes towards the end of the first half when riot police had to step in to stop an attack by Slovan fans on visiting supporters. It was a bittersweet night for Balotelli on his first appearance in City colors. The Italy forward came on as a substitute to score a 72nd-minute winner for his new side, which has spent around 150 million pounds ($234 million) on players since the end of last season. But a dream debut was ruined as he limped off in injury time, accompanied by medical staff. Elsewhere, Massimo Maccarone, Abel Hernandez and Javier Pastore were Palermo's goalscorers in its 3-0 victory against Maribor, FC Porto won by the same scoreline at Genk thanks to goals by Souza and Fernando Belluschi, and Ezequiel Lavezzi scored the winning goal as Napoli edged Elfsborg 1