United will resume their last-16 tie against Madrid on Tuesday following a 1-1 draw in the away leg and Kagawa’s first United treble ensured they will approach the game brimming with confidence.
“He is a good finisher,” said United manager Alex Ferguson of his side’s match-winner.
“His injury in October, November set him back a bit, but he’s getting his form back slowly and gradually. His second and third, in particular, were terrific.”
Ryan Giggs was made to wait for his 1,000th senior appearance after being left out of United’s match-day squad, but Ferguson selected his first-choice strike pairing of Robin van Persie and Wayne Rooney.
The hosts dominated the first half at Old Trafford but they had to wait until first-half stoppage time to take the lead.
Japan international Kagawa claimed the goal, beating Norwich goalkeeper Mark Bunn with a near-post volley after van Persie had helped on Antonio Valencia’s inswinging right-wing cross.
Kagawa doubled United’s tally 14 minutes from time, sweeping home from Rooney’s square pass, and completed his treble in the 87th minute by racing onto a Rooney lay-off and coolly lifting the ball over Bunn.
Rooney got on the score-sheet in the final minute with a beautiful strike into the top-left corner from outside the box to further amplify the task facing second-place Manchester City, who visit Aston Villa on Monday.
Chelsea drew a line beneath interim manager Rafael Benitez’s attack on the club’s fans by winning 1-0 at home to West Bromwich Albion to reclaim third place from Tottenham Hotspur, who host Arsenal on Sunday.
After criticising Chelsea’s fans in mid-week, Benitez was greeted at Stamford Bridge by banners bearing the words ‘Rafa Out’ and ‘The Interim One’ — a reference to beloved former coach Jose ‘The Special One’ Mourinho.
Oscar and Juan Mata both went close for Chelsea in the early stages before Demba Ba scored the only goal in the 28th minute, hooking home from six yards after David Luiz headed Oscar’s deep cross from the left back across goal.
“You can see today the fans were behind the team,” said Benitez.
“There were a lot of positives.”
Bottom club Queens Park Rangers gave their bid to avoid relegation a huge shot in the arm by winning 2-1 at Southampton to close to within four points of safety.
Jay Bothroyd tapped in a cross from Park Ji-sung in the 77th minute to give QPR victory at St Mary’s, after Loic Remy’s 14th-minute opener was cancelled out by Gaston Ramirez’s clever dinked finish on the stroke of half-time.
“It was a big result for us,” said QPR manager Harry Redknapp.
“It’s a difficult place to come and Southampton are a good team, but that’s what you get when you all work hard.”
Reading, second from bottom, received another setback in their fight to avoid the drop as they sank to a third consecutive loss in a 3-1 defeat at Everton.
Marouane Fellaini broke the deadlock with a 42nd-minute header, with Steven Piennar’s fine goal making it 2-0 in the 59th minute.
Pienaar then created Everton’s third in the 66th minute with a through-ball that was converted by Kevin Mirallas, before Hal Robson-Kanu replied for the Royals.
Sunderland, meanwhile, came from two goals down to draw 2-2 at home to Fulham in an open game at the Stadium of Light.
A Dimitar Berbatov penalty and a Sascha Riether strike put the visitors 2-0 up inside 35 minutes, but Craig Gardner immediately reduced the arrears from the penalty spot and Stephane Sessegnon pounced to claim a 70th-minute equaliser.
Elsewhere, substitute Jack Collison gave West Ham United a 1-0 win at Stoke City, while an 85th-minute Luke Moore effort earned League Cup winners Swansea City a 1-0 win at home to Newcastle United.
The late game sees ninth-placed Liverpool visit Wigan Athletic.