Jordan Ayew netted a late penalty to set up a nervous final few minutes, but the Premier League side will fly home happy with a confident performance in Europe.
Arsene Wenger's men earned a win in their last visit to the Stade Velodrome back in 2011, and they replicated the feat Wednesday. Walcott found the net with a close-range volley before Ramsey wrapped things up with a fine individual effort after the break.
Jordan Ayew grabbed a late consolation from the penalty spot for the hosts, but Arsenal held on to claim all three points.
Elie Baup made just one change to the Marseille side that drew 1-1 with Toulouse on Saturday, with Andre Ayew replacing Florian Thauvin on the left side of midfield. Arsenal's only alteration came in defence, with manager Arsene Wenger — who has seen his side win five of its last six competitive outings — opting to select the experienced Per Mertesacker in favor of Carl Jenkinson.
Marseille made a bright start to proceedings with Andre-Pierre Gignac and Mathieu Valbuena both testing Wojciech Szczesny in the early going. Arsenal responded quickly, however, as Walcott forced Steve Mandanda into a save with a close-range effort after beating left back Jeremy Morel with pace.
Still, it was the hosts that continued to dictate play. Valbuena volleyed over before Andre Ayew headed narrowly wide after an excellent right-wing cross from Dimitri Payet. The visitors struggled to gain a foothold in the midfield, with Valbuena and 21-year-old Giannelli Imbula particularly impressive for Baup’s men.
And Marseille almost got its reward for a positive display shortly before the break, with Gignac heading just over the bar at the near post after powering onto a Payet corner.
Arsenal remained an attacking threat, though, and it almost took the lead in superb fashion when Kieran Gibbs was denied by a fantastic reaction save from Mandanda after latching on to a deft back heel from Mesut Ozil.
The game quickly became stretched, with both sides crafting regular goalscoring opportunities. Payet kept Szczesny busy with a fierce drive before Jack Wilshere drew a near-post stop from Mandanda at the other end.
Arsenal never looked settled at the back, and it had Gibbs to thank for keeping it level as he showed great awareness to head a Payet cross off the line after a miscommunication between Mertesacker and Szczesny.
But Marseille was finally made to pay for its profligacy 19 minutes into the second half when Walcott fired a magnificent volley into the top corner after Morel had failed to deal with Gibbs' far-post cross.
Payet and Valbeuna both then came close as the Ligue 1 club searched for an equalizer, but it was Arsenal that proved the more clinical of the two sides. Ramsey secured the points as he jinked through the defense before sending a precise low shot beyond the grasp of Mandanda.
Marseille did get one back in injury time, though, with Jordan Ayew scoring from 12 yards after Laurent Koscielny had felled Andre Ayew in the box.