Di Maria fired the French champions into the lead with a freak goal and Zlatan, with two, Lucas and Lavezzi also fired home, marking 12 games without a loss in 2015-16 so far.
Chances were few and far between at Roazhon Park as the league leaders PSG stuttered to a narrow victory over the team from Rennais to maintain their unbeaten tag.
Ross Barkley, Alex Oxlade-Chamberlain and an Arlauskis own goal saw the Three Lions past the Baltic nation, ensuring a blemish-free record at the end of Group E.
The European Championship hosts continued their impressive tournament preparations as Didier Deschamps' men’s early rally secured victory in Copenhagen on Sunday.
The Bayern Munich striker scored the winner and also levelled David Healy's record for a single qualifying competition as his nation booked their place in France.
Thomas Muller's effort early in the second half was swiftly cancelled out by a Jaba Kankava strike, but Joachim Low's men ultimately avoided slipping behind Poland in their group.
Victory means the Oranje are now in third place in Euro 2016 Group A, but Turkey will overtake them if they win their game in hand.
The Chelsea attacker was one of four separate goalscorers for the visitors as they overcame the Iberian nation to qualify for the finals in France next year.
The 2006 World Cup winners ran out comfortable winners over the hosts, sending them to the tournament proper in France despite a first-half scare.