The skipper overhauled the mark previously set by Ruud van Nistelrooy when he opened the scoring ten minutes before the break.
He set up Juan Mata to double the lead and further strikes from Zlatan Ibrahimovic and Jesse Lingard ensured the Reds overhauled the Eredivisie leaders in the Group A standings.
United are second - two points ahead of the Rotterdam side and one point behind Fenerbahce - and require only a draw from the trip to Zorya on Matchday Six to seal our spot in the last 32.
The Reds remain in contention to progress as group winners, should we beat Zorya and Fenerbahce share the points with the De Kuip club.
The Reds started strongly and soon brought out the best in Feyenoord's former Liverpool keeper Brad Jones who saved superbly in quick succession from Paul Pogba and Michael Carrick.
Pogba headed over before the visitors, who had barely threatened up until that point, burst into life on the hour-hark mark.
Eljero Elia picked out Nicolai Jorgensen who forced a fine save from stand-in stopper Sergio Romero, who then did even better to brilliantly deny Dirk Kurt on the follow up with his foot.
That intervention proved crucial as United moved in front in the 35th minute as Ibrahimovic picked out Rooney - just onside - to clip home over the advancing Jones.
Ibrahimovic had an effort blocked and Henrikh Mkhitaryan, who dazzled throughout, then should have earned a penalty having been hauled down by Jans Toomstra following a brilliant run from deep.
Mkhitaryan fired into the side netting and a frantically back-pedalling Jones tipped over Mata's dedicate lob as United up the ante in pursuit of the elusive second goal.
It duly arrived in the 69th minute as the Spaniard - who also had a goal disallowed - slid home his second goal in as many games from Rooney's cross at the culmination of a scintillating team move.
Jones saved well from substitute Jesse Lingard before another replacement, Marcus Rashford, found Ibra who fired in the third with the aid of a deflection off the unfortunate keeper.
Jesse was not to be denied, however, and put the gloss on another wonderful exchange of passes with a delightful finish late on to put United in a strong position in the group.
Overall team performance: 8.5/10
United Faithful Man of the Match: Henrikh Mkhitaryan. We've waited a long time to see the £26 million man at his best, but it was worth it. Received a deserved ovation when taken off late on.