Niall Quinn, a defender with big potential, scored the opening goal for David Jeffrey's side with a superb free-kick.
The Blues made it 2-0 just before the interval when Billy Joe Burns saw his cross loop off Andy Hunter's head for an unlucky own goal.
Brian McCaul headed in a third for Linfield and substitute Ryan Henderson - with his first touch - made it four.
The one black spot on the evening for the champions was another injury to Matthew Tipton.
The ex-Portadown player had only been on as a substitute for 11 minutes when he was forced off with what looked like a twisted knee.
Leaders Cliftonville ensured their strong start to the season continued, beating Donegal Celtic 3-1.
George McMullan gave the Reds the lead in the 42nd minute from the penalty spot after Darren McNamee's foul on Ryan Catney.
McMullan made it two when his shot was deflected in.
Joe Gormley out-foxed McNamee to make it three, before Mark Miskimmin scored a DC consolation.
Ballinamallard United now have four wins in succession after beating Glenavon 2-1.
They opened the scoring in this match just 47 seconds in when Ryan Campbell shot past visiting goalkeeper Andy Coleman.
With 25 minutes left for play Jason McCartney made it 2-0 with a close-range finish.
Leon Carters handled the ball in the box and was sent-off on 89 minutes, with Kyle Neill scoring the resultant penalty, however it proved mere consolation.
Ballymena United staged a late, late show in taking a point from their 1-1 draw with Glentoran at the Showgrounds.
David Howland's brilliant second-half strike looked like it would provide the Glens with all three points, however Gary Thompson scored, getting a touch on David Cushley's ball.
Portadown secured their first Premiership win since the first day of the season when Darren Murphy's header was the only goal of the match against Crusaders.
The Crues had chances when Paul Heatley tested goalkeeper David Miskelly and Gary McCutcheon headed over, but the Ports held on for all three points.
Elsewhere, Coleraine are on level points with Cliftonville thanks to this comfortable win on Saturday.
Coleraine went ahead on 14 minutes after Stephen Lowry fired beyond Niall Morgan after a header on from Darren Boyce.
The lead was doubled just six minutes later when Paul Owens latched onto Curtis Allen's flick on.
Goalkeeper Gavin Cullen then denied Dungannon's Michael Kerr as Coleraine reclaimed second spot on goal difference.
Dungannon remain in eighth place with just two wins from their nine league matches.
Results in full:
Friday 28 September:
Ballymena United 1 - 1 Glentoran
Ballymena Utd: Thompson 93.
Glentoran: Howland 49.
Cliftonville 3 - 1 Donegal Celtic
Cliftonville: McMullan 45 (penalty), 51, Gormley 53.
Donegal Celtic: Miskimmin 73.
Linfield 4 - 0 Lisburn Distillery
Linfield: Quinn 20, Hunter og 41, McCaul 68, Henderson 78.
Portadown 1 - 0 Crusaders
Portadown: Murray 23.
Ballinamallard United 2 - 1 Glenavon
Ballinamallard Utd: Campbell 1, McCartney 65, Carter sent off 88.
Glenavon: Neill 89 (penalty).
Saturday 29 September:
Coleraine 2 - 0 Dungannon Swifts
Coleraine: Lowry 14, Owens 20