First-half goals from Robbie Garrett and Mark McAllister gave the defending champions a two-goal cushion at the break at Stangmore Park, before David Armstrong added a third in the 57th minute.
The hosts hit back eight minutes later when Johnny Topley headed home from a corner, but Linfield substitute Rory Patterson put the gloss on another comfortable win for David Jeffrey's side when he grabbed the fourth goal in the final minute of normal time.
At the Oval, Donegal Celtic found themselves 2-0 up inside a four minute spell in the second half of their game against Glentoran.
Johnny Harkness scored the first with a 54th minute free-kick, before Darren Murray doubled the visitors' advantage in the 58th minute.
The Glens had been reduced to ten men a minute before Murray's strike.
Gary Hamilton's 62nd minute penalty gave the hosts hope, but they were unable to convert late pressure into goals as DC held on to claim all three points.
Elsewhere, Lisburn Distillery claimed their first win of the season with a 3-2 win over the Coleraine at the Showgrounds.
The Bannsiders opened the scoring through Curtis Allen in the seventh minute, but the hosts levelled in controversial circumstances when Gary Liggett fired in a cracking drive midway through the second half.
Coleraine had put the ball out of play following an injury to a Distillery player, but rather than throw the ball back to the opposition, Mark Patton instead found one of his own players to, in turn, teed up Liggett to fire in from the edge of the area.
However, Liggett's afternoon came to an abrupt end nine minutes later when he was sent off for a second bookable offence after kicking the ball away.
Another long-range effort, this time from David Cushley, gave the visitors the lead, but Coleraine looked to have done enough to earn a draw when Stephen Lowry scored with a low half-volley three minutes from time.
However, Distillery responded right from the restart when Patton struck a looping shot over Michael Doherty to wrap up a 3-2 win.
At Mourneview Park Carrick Rangers picked up their first win of the season at the expense of Glenavon.
Stephen O'Neill grabbed the opener for Carrick in the 44th minute, before Paul Owens struck in the 65th minute with an early contender for goal of the season - cracking a fierce half-volley into the Glenavon goal.
Andy Graham grabbed a consolation goal for the hosts in the 79th minute, but Carrick held on for a 2-1 victory.
In Saturday's other games first-half goals from Timmy Adamson, Jordan Owens and Chris Morrow sealed a 3-0 away win for Crusaders against Ballymena United, while Matthew Tipton and Wesley Boyle were on target for Portadown as they secured a 2-0 win over Cliftonville at Solitude.
IFA Carling Premiership Results:
Ballymena United 0-3 Crusaders
Crusaders: Adamson 9, Owens 31, Morrow 44
Cliftonville 0-2 Portadown
Cliftonville: McMullan sent off 25
Portadown: Tipton 50, Boyle 53
Braniff sent off 56
Coleraine 2-3 Lisburn Distillery
Coleraine: Allen 7, Lowry 87
Lisburn Distillery: Liggett 61, Cushley 75, Patton 87
Liggett sent off 70
Dungannon Swifts 1-4 Linfield
Dungannon: Topley 65
Linfield: Garrett 10, McAllister 37, Armstrong 57, Patterson 90
Glenavon 1 - 2 Carrick Rangers
Carrick: O'Neill 44, Owens 64
Glenavon: Graham 79
Glentoran 1-2 Donegal Celtic
Glentoran: Hamilton (penalty) 62
Taylor sent off 57
DC: Harkness 54, Murray 58