Europa League holders Atletico Madrid enjoyed a convincing start to the group phase as Athletic Bilbao and Inter Milan were both held at home.
Napoli and Bordeaux were among the teams to be in free-scoring mood, but the likes of Borussia Monchengladbach and Bayer Leverkusen endured frustration in front of goal.
In Group A, Udinese snatched a 1-1 draw at home to in-form Russian Premier League side Anzhi Makhachkala, Antonio Di Natale equalising in injury-time after Lacina Traore put the Russians ahead on the stroke of half-time.
Liverpool secured a thrilling 5-3 victory over Young Boys after substitute Jonjo Shelvey scored twice in the closing 15 minutes in Switzerland.
In Group B, holders Atletico Madrid got the defence of their title up and running in fine style with a 3-0 win over Hapoel Tel Aviv in Israel.
Atletico, unbeaten so far in the Spanish Primera Division, took a 37th-minute lead through Cristian Rodriguez and Diego Costa added a second before the break. Raul Garcia notched the third in the 63rd minute.
In the other match in Group B, Czech Liga leaders Viktoria Plzen came from behind to beat Portuguese side Academica 3-1. Wilson Eduardo put Academica in front before Pavel Horvath, Michal Duris and Frantisek Rajtoral replied.
Napoli, currently second in Serie A, claimed an emphatic 4-0 win over AIK in Group F with a hat-trick from Eduardo Vargas and a fourth from Blerim Dzemaili in injury-time.
But experienced European campaigners PSV Eindhoven were surprised by a 2-0 defeat by Dnipro Dnipropetrovsk in Ukraine, with Matheus Nascimento and an Atiba Hutchinson own goal doing the damage.
Bordeaux matched Napoli's margin of victory with a 4-0 win over Club Brugge in Group D, the goals coming from Ludovic Sane, Yoan Gouffran, Jussie and an own goal from Bjorn Engels.
In the same group, Newcastle failed to find a way past Maritimo and had to settle for opening their Europa League account with a goalless draw at the Estadio dos Barreiros.
Group C opened with a pair of draws, Marseille coming back from 2-0 down to grab a 2-2 draw away to Fenerbahce, and AEL and Borussia Monchengladbach battling out a goalless stalemate in Cyprus.
There was another draw in Group E, where Stuttgart and Steaua Bucharest shared a 2-2 tie in Germany, while FC Copenhagen edged past Molde 2-1 in Denmark thanks to a 74th-minute winner from Andreas Cornelius.
In Group H, Japanese defender Yuto Nagatomo came to Inter Milan's rescue with an injury-time equaliser to deny Rubin Kazan a famous win in the San Siro.
The Russians led first through Alexander Ryazantsev's early strike, and despite Marko Livaja's equaliser, the visitors must have thought they had won it when Salomon Rondon scored their second six minutes from time.
But Nagatomo pounced two minutes into added time to secure a face-saving 2-2 draw for the hosts in a group which also saw a goalless opening game between Partizan and Neftchi in Belgrade.
Last year's runners-up Athletic Bilbao also had a lucky escape in their Group I opener against Israelis Hapoel Kiryat Shmona at the Estadio San Mames.
Adrian Rochet put the little-known visitors in front after 14 minutes and it took a 40th minute equaliser from Markel Susaeta to salvage a 1-1 draw.
Also in Group I, Lyon edged Sparta Prague 2-1 with second-half goals from Bafetimbi Gomis and Lisandro Lopez, with Ladislav Krejci replying late for the Czechs.
Tottenham boss Andre Villas Boas was left fuming as his side had three efforts from Clint Dempsey, Jermain Defoe and Steven Caulker disallowed in a goalless draw against Lazio at White Hart Lane.
Also in Group J, Slovenians Maribor had better fortune as they beat Panathinaikos 3-0 with goals from Robert Beric, Agim Ibraimi and a Marcos Tavares penalty.
Sporting held on for a goalless home draw against Basel in Group G despite having Brazilian Xandao sent off after 40 minutes, while Genk eased to a 3-0 home win over Videoton.
Hannover hit back from two goals down to salvage a 2-2 draw away to FC Twente in Group L, while a 40th-minute goal from Juanfran gave Levante a 1-0 win at home to Helsingborg.
Group K saw a 2-1 win for Rosenborg at Rapid Vienna and a goalless draw between Bayer Leverkusen and Ukrainians Metalist Kharkiv in Germany.