Meanwhile, defending champions Chelsea travel to FC Nordsjaelland of Denmark, while Manchester United are also on the road to Cluj.
London: The Champions League is only one round old and already AC Milan and Manchester City are under pressure to deliver victories this week, for very different reasons.
After opening with a lackluster 0-0 home draw with Anderlecht and languishing in mid-table in the Italian league, Milan coach Massimiliano Allegri's job is at risk as the seven-time European champions make the tricky trip to Zenit St. Petersburg on Wednesday.
Roberto Mancini's position as City manager isn't under threat but his team's place in Europe's premier club competition certainly will be if the English champions fail to beat Borussia Dortmund on the same night.
City lost 3-2 to Real Madrid in a thriller a fortnight ago and with Dortmund having opened up with a win over Ajax, Mancini's team cannot afford another slip-up.
Of the continent's other top teams, only defending champions Chelsea failed to get off to a winning start on the first matchday — drawing 2-2 with Juventus at Stamford Bridge — but it will be a major surprise if the Premier League leaders don't come away with a victory at tournament debutant FC Nordsjaelland of Denmark in Group E.
Buoyed by their superb 3-2 comeback win over Sevilla on Saturday in the Spanish league, Barcelona head to Benfica looking to stay perfect in Group G while Manchester United manager Alex Ferguson may be tempted to partner strikers Robin van Persie and Wayne Rooney for the first time in the team's trip to Romanian outsider Cluj in Group H.
Much of the focus this week, though, will be on what is widely viewed as the toughest of all eight groups, involving Real and City — who served up a wild shootout when they met two weeks ago in the Spanish side's 3-2 win at the Santiago Bernabeu.
That result put Real's campaign back on course after a wobbly start, with the Spanish champions away at Ajax next, but left City in early trouble in the Champions League even after just one game.
If Dortmund win at the Etihad Stadium, a second straight group-stage elimination is likely on the cards for an ambitious, wealthy club whose sights are set on mastering Europe after ending a 44-year wait for a domestic league title last season.
City have yet to keep a clean sheet this campaign, putting pressure on their star-studded forward line.
"Everyone spoke well about City for one year and now it's negative because we are used to winning every game, scoring lots of goals, not conceding many goals," Mancini said. "But this is normal. We are not worried about this.
"The group is very difficult. We didn't start too well because we lost against Real Madrid and for this reason it is important to play well against Dortmund."
Milan, a decorated club very much at the other end of the rich list nowadays, gave up the lead in a 1-1 draw at Parma on Saturday to leave the Rossoneri with just two wins in six Serie A matches. Club president Silvio Berlusconi's trigger finger is believed to be getting twitchy.
"If we're not able to win matches like these, it means something is wrong," Allegri said.
Milan are struggling to overcome the loss of an entire squad's worth of top players including the likes of Zlatan Ibrahimovic and Thiago Silva, who both bolted for Paris Saint-Germain in the summer. Stalwarts Alessandro Nesta, Gennaro Gattuso and Clarence Seedorf also left.
A win in Russia, though, could be the result that sparks Milan's season, with a city derby against Inter coming up next weekend.
Malaga are the Group C leader after beating Zenit 3-0 and travel to Anderlecht unbeaten in their last nine games in all competitions, despite the exit of several players in the offseason to balance the books.
PSG had the most impressive victory on matchday one, thrashing Dynamo Kiev 4-1 in Group A, but should find things much tougher at Porto next.
The big-spending French side is undefeated this season and, in Ibrahimovic, has a striker with seven goals in eight games since his Milan move.
"I hope to win the Champions League with PSG one day, it's what I train for every day," the Sweden international said.
Group B favorite Arsenal host Olympiakos while Schalke are at home to Montpellier in the other match.
In Group F, beaten 2012 finalists Bayern Munich look to back up their 2-1 win over Valencia two weeks ago when they visit BATE Borisov, with Valencia hosting Lille.