Arsene Wenger's men earned a win in their last visit to the Stade Velodrome back in 2011, and they replicated they feat on Wednesday, Walcott finding 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, Andre Ayew replacing Florian Thauvin on the left-hand side of midfield.
Arsenal's only alteration came in defence, with manager Arsene Wenger - who has seen his side win five of their last six competitive outings - opting to select the experienced Per Mertesacker in favour 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, Theo Walcott forcing Steve Mandanda into a save with a close-range effort after beating left-back Jeremy Morel for 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 their reward for a positive display shortly before the break, Gignac heading just over the bar at the near post after powering onto a Payet corner.
Baup's side continued in the ascendancy straight after the break, Rod Fanni volleying inches wide of the post after good work down the right from Alaixys Romao.
Arsenal remained an attacking threat, though, and they almost took the lead in superb fashion, Kieran Gibbs denied by a fantastic reaction save from Mandanda after latching on to a deft backheel from Mesut Ozil.
The game quickly became stretched, with both sides crafting regular goalscoring opportunities, Payet keeping 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 they had Gibbs to thank for keeping them level as he showed great awareness to head a Payet cross off the line after miscommunication between Mertesacker and Szczesny.
But Marseille were finally made to pay for their profligacy 19 minutes into the second half, Walcottfiring a magnificent volley into the top corner after Morel had failed to deal with Gibbs' far-post cross.
Payet and Valbeuna both then went close as the Ligue 1 club searched for an equaliser, but it was Arsenal who proved the more clinical of the two sides, Ramsey securing the points as he jinked through the home defence before sending a precise low shot beyond the grasp of Mandanda.
Marseille did get one back in injury time, though, Jordan Ayew scoring from 12 yards after Laurent Koscielny had felled Andre Ayew in the box.