United, in search of a first FA Cup in 11 years, will face Preston North End in the last 16.
The hosts took the lead after 25 minutes when Mata spread the ball wide to Angel Di Maria and then got himself into the box to flick home from Marouane Fellaini’s nod-down.
The lead was doubled less than ten minutes later when Rojo headed home his first Manchester United goal from a delightfully dinked Robin van Persie cross.
Then substitute Wilson put the game to bed after 73 minutes when he picked the ball up on the edge of the box, shifted onto his left foot and fired a well-placed shot into the bottom right corner.
Kick-off was pushed back to 8.05pm as the 7,000 Cambridge fans were held up on their way to the ground and by 8.06pm the visitors had wasted their one glorious chance. Daley Blind was robbed of possession and Elliott was put clear through on goal but he could only stroke the ball onto the post.
1’ - WHAT A CHANCE! Cambridge almost take the lead after less than a minute! Daley Blind is robbed and Tom Elliott is clear through on goal but can only find the post! What a start that would have been!
Cambridge United's Tom Elliott (L) shoots at goal during their FA Cup fourth round match against Manchester United at Old Trafford (Reuters)
Image credit: Reuters
25’ - GOAL! Manchester United 1-0 Cambridge. Di Maria crosses it, Fellaini nods it down, Mata pokes it home. Simple.
30’ – Man Utd nearly double their lead! Di Maria strolls past his man on the left and cuts back for Mata, who miscues. Then McNair rushes onto a ball but his blazed shot is deflected out for a corner.
32’ - GOAL! Manchester United 2-0 Cambridge. The hosts do double their lead! It's a first goal for Rojo in a red shirt as he heads home from a dinked cross from van Persie, who had picked it up inside the box from a corner.
54’ - Danger for Cambridge! Rooney has it on the edge of the box and tees himself up for a volley. Dunn does well to stop it and get out to deny van Persie the follow-up.
64’ - Great save! Dunn denied Man Utd for 90 minutes in the original tie and here he excels himself once more, getting his hands to an effort from van Persie, who had brought the ball down on the run and fired off a quick shot.
68’ - Another great save from Dunn! Di Maria spanks one from range and the Cambridge keeper leaps into the air and tips the ball over the bar.
73’ - GOAL! Manchester United 3-0 Cambridge. The game is put to bed and it's substitute Wilson who scores it with a well-placed left-footed shot into the bottom right corner from the edge of the box.
Manchester United's Marcos Rojo, left, celebrates scoring
Image credit: PA Sport
There are 54 league places between Manchester United (3rd in Premier League) and Cambridge United.
Luke Chadwick started a game at Old Trafford for the first time in over 13 years.
Manchester United have lost just one of their last 42 FA Cup matches against lower league opponents (W34 D7 L1).
Man Utd and Cambridge had only ever met once before in any competition before this tie and that was the 1991-92 League Cup where the Red Devils won 4-1 on aggregate over two legs.
The 1991-92 season was also the last time Cambridge knocked a top flight team out of the FA Cup when they beat Coventry City after a replay.
Manchester United's James Wilson celebrates after scoring a goal against Cambridge United during their FA Cup fourth round soccer match at Old Trafford in Manchester, northern England February 3, 2015 (Reuters)
Image credit: Reuters
We can’t expect giant-killings all the time. The fourth round has already given us plenty. Chelsea crashed out at the hands of Bradford and Middlesbrough dumped out Man City. Losing the current top three Premier League teams in one round would have always been too much to ask. The original tie at the Abbey stadium was special enough, and this fourth round has reaffirmed our faith in the magic of the FA Cup.
Paddy McNair (Manchester United): The youngster was always at the heart of things as Louis van Gaal employed a game-plan revolving around width and crosses. The full-back bombed forward all night, ever-confident and producing mostly decent crosses.
Manchester United: De Gea 7, McNair 8, Smalling 6, Evans 6, Rojo 7, Blind 7, Fellaini 7, Mata 7, Rooney 7, Di Maria 7, van Persie 7…Subs: Herrera 6, Young 6, Wilson 8.
Cambridge United: Dunn 8, Tait 7, Coulson 6, Nelson 6, G Taylor 6, Donaldson 7, Champion 6, McGeehan 6, Simpson 6, Chadwick 6, Elliott 6…Subs: Miller 6, Morrissey 6, Kaikai 6.