The £25million man scored twice before delivering a succulent cross for Marouane Fellaini to head home in the final seconds of the match, securing Manchester United a vital 3-1 win over Club Brugge.
Depay produced the match-winning wearing the famous United No.7 shirt, formerly worn by the likes of Beckham, Cristiano Ronaldo and Eric Cantona.
And Depay, who has already formed comparisons to Ronaldo, is whipping in crosses like Beckham used to, according to Ferdinand.
With the final goal in the closing stages, Ferdinand also believes that the Red Devils are set to comfortably make the group stages of the competition, returning at the first time of asking.
Speaking as a pundit on BT Sport, he said: "I think United will feel relief with that result more than anything.
"I think going over to Bruges at 2-1 would have been a very dangerous and nervy experience for this team.
"Memphis has shown now what he's capable of and he's shown that there's more to his game than just taking people on and shooting. He can deliver a great ball into the box too as with the last goal.
Alex Livesey/GettyCrucial: Fellaini heads home in the 94th minute from Depay's cross
"That cross was [David] Beckham-esque with the bend and whip. You haven't got to beat players but kids these days watch YouTube and just want to do that all the time. He just put that on a six-pence. Beautiful.
"I think the thing that excites you as well is that you can see he wants to be a star, he wants to be the main man, he wants the ball all the time, he wants to be the man at the end of moves who shoots and scores.
GettyDelivery: Beckham was iconic for the quality of his delivery
"This crowd love and warm to people like that - you've seen it over the years with the likes of [Cristiano] Ronaldo and [Wayne] Rooney."
Fellow BT pundit Paul Scholes was equally as complimentary to United's new signing.
Tom Purslow/Man UtdNew 7 in town: Memphis has taken the iconic United number
He said: "He was brilliant tonight and that's what United fans want to see - somebody that excites you, somebody that gets you on the edge of your seat and he also produced a great cross at the end for Fellaini as well."
"He looks brilliant from what I've seen tonight, showing a great bit of skill and composure for the first goal."
The second leg of the Champions League qualifier takes place next Wednesday night, before United face the prospect of a tricky group draw.