Holders Barcelona left it late to snatch a 1-1 Champions League draw at Werder Bremen while a Didier Drogba hat-trick guided Group A rivals Chelsea to a convincing 3-1 win over Levski Sofia on Wednesday.
The place to be for excitement, though, was Anfield where Liverpool led Galatasaray 3-0 early in the second half before squeezing home 3-2 in a heart-stopping finale.
Inter Milan had two men sent off as they slumped to their second consecutive defeat with a 2-0 loss to Bayern Munich at San Siro, Serie A rivals AS Roma went down 2-1 at Valencia and PSV Eindhoven came away with a 1-0 win at Girondins Bordeaux.
The first Champions League match on an artificial pitch finished with Spartak Moscow drawing 1-1 at home to Sporting Lisbon while Shakhtar Donetsk drew 2-2 with Olympiakos Piraeus.
It was not a happy night for Barca, who trailed to a 56th minute own goal by captain Carles Puyol and then lost Cameroon striker Samuel Eto'o to a knee injury in a game where Werder had the upper hand.
Argentina teenager Lionel Messi spared the European champions' blushes a minute from time, working a one-two with Deco before threading the ball past goalkeeper Tim Wiese.
Barcelona coach Frank Rijkaard said: "We fought hard and right up to the end and managed to come away with a good result...it was deserved."
Drogba's hat-trick put Chelsea firmly on course for the knockout rounds, leaving them on six points -- two more than Barca and five clear of luckless Werder.
The Ivory Coast striker volleyed home a loose ball in the 39th minute, squeezed a shot beneath keeper Georgi Petkov after the break and turned in the third off a shot by Frank Lampard.
A late Levski rally brought a consolation goal for Mariyan Ognyanov but Chelsea coach Jose Mourinho was satisfied.
"It was cool, calm and composed although we are still not playing very, very well," he said.
The night's results will add extra spice to Chelsea's next match, at home to familiar foes Barca. The clubs have met in the previous two seasons -- with the honours being shared.
Liverpool and PSV have four points after the second round of games in Group C, although their wins on Wednesday could not have been more different.
Two goals by lanky England striker Peter Crouch and a Luis Garcia header gave Liverpool a seemingly unassailable lead with just over half an hour to play -- only for substitute Umit Karan to score twice in six minutes with a couple of headers.
Liverpool, Champions League winners in 2005, could even have been held to a draw as the rampant Turkish side poured forward.
A single goal was enough for PSV, scored by Finn Mika Vaeyrynen, though they had to play the last five minutes with 10 men after a red card for defender Michael Lamey.
Things are clearly not working out for Serie A leaders Inter, who had Sweden striker Zlatan Ibrahimovic and Italy defender Fabio Grosso sent off in captain Javier Zanetti's 500th appearance for the club.
Late strikes by Claudio Pizarro and Lukas Podolski secured the points for the Bundesliga champions in Group B, which Bayern lead with six points -- two more than Sporting.
First half goals from Miguel Angel Angulo and David Villa, either side of a Francesco Totti penalty, gave Valencia their second successive victory and top slot in Group D.