The striker, who will meet up with Roy Hodgson’s squad on Monday, pulled a goal back for the Reds late on after two Juan Mata goals had given United a two-goal advantage.
Mata’s strike 15 minutes in gave the Red Devils the lead, leading to Brendan Rodgers to introduce former Three Lions captain Steven Gerrard from the bench at the break.
But just 48 seconds into the second half Gerrard was given his marching orders after a stamp on Ander Herrera.
Mata produced a brilliant scissor-kick finish to double his side’s advantage before Sturridge pounced late on to set-up a nervy finish, but it was the visitors who had the best opportunity to add to the scoreline.
Rooney saw his penalty saved
In the dying stages United, who had Three Lions internationals Michael Carrick, Phil Jones and Chris Smalling in their side, were awarded a penalty. England captain Wayne Rooney put the ball down but saw his spot-kick saved, but his he and his team-mates held on to take all three points.
“I take full responsibility and reacted wrong,” Gerrard told Sky afterwards. “I’ve let my team-mates and my manager down.
“I’ve come out here now to apologise to the fans and everyone in the dressing-room.”
Liverpool, who started with Adam Lallana, Jordan Henderson and Raheem Sterling in their line-up, now trail fourth-placed United by five points.
Later in the afternoon, Chelsea maintained their six-point lead at the top of the table as they defeated Hull City 3-2 at KC Stadium.
The visitors, who had England centre-back Gary Cahill in their defence, went two goals ahead after Eden Hazard fired in and Diego Costa curled in his 20th goal of the season.
But Hull replied with two goals in 74 seconds as Ahmed Elmohamady slid in before Abel Hernandez took advantage of a goalkeeping error to equalise.
But Loic Remy came off the bench to net a late winner for Jose Mourinho's side.
And in west London, Aaron Lennon's first goal for Everton secured them a win over QPR.
England Under-21s defender John Stones, and senior Three Lions men Phil Jagielka and Leighton Baines all started for the Toffees. Ross Barkley, another member of Hodgson's squad for the clashes against Lithuania and Italy, came on as a second half sub.
Rob Green, who was yesterday called up to the seniors to replace Fraser Forster, was in goal for the R's.
