The Dutchman was handed a rare start and impressed as United emerged 4-1 victors in Group H.
A Bruno Fernandes brace, including a stunning first-time half-volley from the edge of the box, put United 2-0 ahead at Old Trafford, before Marcus Rashford added the hosts’ third from the penalty spot.
Istanbul pulled one back when David de Gea failed to prevent a Deniz Turuc free-kick from crossing the goal line, but Dan James rounded out the scoring for the Red Devils in added time of the second half.
And although Van de Beek was not among those to score or record an assist, his performance caught the eye of Hargreaves.
“Van de Beek is so unselfish that he can just fit in,” said the former United midfielder on BT Sport.
“I think he’s played himself into the starting line-up.”
Ex-United defender Ferdinand added: “I was really was pleased with him.
“We’ve been impatient ourselves, but Ole [Gunnar Solskjaer] has shown why he has been thought of so highly.
“He's the one player that can play one-touch, two-touch and keep it simple. He sacrifices parts of his game to help other people and you need that in great times.
“He’s the one player that will make other players play well.”
Ferdinand and Hargreaves’ former United team-mate Paul Scholes was also full of praise for the former Ajax man, saying: “Some of the one-touch stuff was brilliant.
“He had the awareness around him to find [Edinson] Cavani and find some good balls to Marcus [Rashford].
“What we saw tonight was his best position; I think he’s good enough at the defensive position.
“He will be willing to try to do that. But it won’t be the defensive quality he brings, he will be bringing stuff going forward.”