Jim Smith's side were put under pressure for large parts of the game but defended solidly and took the chances that came their way with confidence.
After a bright start by Morecambe, the visitors, who included former Premiership star Rufus Brevett in their line-up for the first time, were gifted a first midway through the first half and never really looked back.
It was former Preston front man Steve Basham who gave the U's the lead with a real poacher's goal. A deep through ball from Andy Burgess should have caused the Morecambe defence no problems but Danny Meadowcroft saw his attempted header back to goalkeeper Ryan Robinson fall short and Basham nipped in between the two to head into an empty net.
The visitors added a second 10 minutes later after some more indifferent Morecambe defending following a good run from Burgess which ended with a corner. Carl Pettefer delivered his cross to the far post and Chris Willmott's header was fumbled by Robinson for Phil Gilchrist to take full advantage and nod home the loose ball from close range.
There was little Morecambe could about Oxford's third when Burgess showed his quality with a fine strike three minutes into injury time. Burgess collected the ball on the right hand side and curled a lovely effort past Robinson's right hand.
Oxford could even have made the long journey home with another goal to their credit after they were awarded a penalty on 49 minutes when the diminutive David Perkins was adjudged to have climbed over Marvin Robinson. Fortunately for Morecambe Robinson guessed correctly and saved Basham's poorly struck spot-kick.
But although the score line looked convincing Morecambe had their fair share of possession and chances.
The closest the came to pulling one back was when Danny Carlton headed a dangerous Adam Yates cross against the woodwork and in the end there was a feeling that this just wasn't going to be their day.