The Blues found the top-flight newcomers tough to break down in the opening exchanges, but eventually went ahead in the 35th minute when Aaron Burns set up Mark McAllister to fire the opening goal.
Burns doubled Linfield's advantage eleven minutes from time after being set up by Rory Patterson, and the former Plymouth Argyle man was again the provider as McAllister grabbed his second goal near the end to seal a 3-0 victory.
Portadown, meanwhile, earned a superb 3-0 victory over Crusaders at Seaview, with the league's top scorer Matthew Tipton again on target.
The Welshman netted the opener in the 17th minute when he got the final touch to Tim Mouncey's glancing header.
Kevin Braniff added a second with a superb volley in the 36th minute, and the striker wrapped up the win with his second just after the break, although there was a hint of controversy as he appeared to handle the ball before getting his shot away.
At the Oval, Glentoran's woes continued as they suffered a 4-2 home defeat to Ballymena United.
David Howland opened the scoring for the hosts with a goal in the 35th minute, before Gary McCutcheon equalised with a strike seven minutes after the break.
The veteran striker headed home in the 72nd minute, but Glens substitute Andrew Waterworth fired in the equaliser five minutes later.
However, the Sky Blues were not to be denied, and McCutcheon turned provider eight minutes from time when his cross was headed in at the back post by Allan Jenkins.
McCutcheon completed his hat-trick with a goal two minutes later.
While things look grim for Glens boss Scott Young, there was an upturn in fortunes for Glenavon manager Marty Quinn, who saw his side pick up their first league win of the campaign.
Andy Graham's seventh minute goal helped the Lurgan blues to a 1-0 victory at home to Coleraine, although they did well to hold their lead after playing the whole of the second half with ten men following Ryan Harpur's sending off for a second yellow card.
In the game at Solitude, Donegal Celtic held off a second half fightback to earn a 3-2 win over Cliftonville.
A volley in the opening minute from Ryan Henderson put the visitors in front, before a great strike from Eamonn McAllister made it 2-0 in the 13th minute.
DC found themselves up against it when Darren Murray was sent off for an apparent head-butt on Ciaran Caldwell just before half time, and the Reds got back into the game with a goal from Ronan Scannell early in the second half.
Rory Donnelly headed the equaliser with four minutes to go, but Henderson had the final say with when he hit the winner two minutes later.
Elsewhere, a 41st minute header from Gary Liggett and a superb strike in second half injury time from substitute Jordan Hughes earned Lisburn Distillery a 2-0 victory over Dungannon Swifts at Stangmore Park.
IFA Carling Premiership Results:
Cliftonville 2 - 3 Donegal Celtic
Cliftonville: R Scannell 57, Donnelly 84.
Donegal Celtic: Henderson 1, 86, McAllister 13, Murray sent off 42.
Crusaders 0 - 3 Portadown
Portadown: Tipton 15, Braniff 37, 47.
Dungannon Swifts 0 - 2 Lisburn Distillery
Lisburn Distillery: Liggett 41, Hughes 91.
Glenavon 1 - 0 Coleraine
Glenavon: Graham 7, Harpur sent off 45.
Glentoran 2 - 4 Ballymena Utd
Glentoran: Howland 35, Waterworth 77.
Ballymena Utd: McCutcheon 61, 71, 84, Jenkins 81.
Linfield 3 - 0 Carrick Rangers
Linfield: McAllister 35, 90, A Burns 79.