The first half was an open affair and Chris Curran had a great chance to put the Mallards in front in the 18th minute but he fired over from eight yards out with the goal at his mercy.
Full back Danny Keohane also hit the post in the first half while striker Ryan Campbell drilled wide as the Mallards pressed.
Linfield though were creating chances of their own and it took some fine goalkeeping from Alvin Rouse to deny them. The Mallards netminder pulled off a great save from Peter Thompson while he then pushed another effort from Thompson away for a corner.
From the resultant corner in the 40th minute though Linfield took the lead as Gault headed home from Carvill's cross.
The lead though was short-lived as the Mallards levelled on the stroke of half time as Crawford confidently slotted home.
The half-time break saw in the region of 30 Linfield supporters staging a Union flag protest in the middle of the pitch, a protest which lasted the duration of the interval before they walked off.
It was Linfield though who took control of matters in the second half and a well worked free kick saw Carvill head home in the 59th minute to put the Blues 2-1 ahead.
And they wrapped things up in the 76th minute as Carvill smashed home his second from 20 yards out to secure the three points for Linfield.