The Blues had to come from behind at Mourneview Park on Saturday afternoon as Guy Bates grabbed the opener when he headed in Andy McGrory's cross in the 22nd minute.
Glenavon could have been 2-0 up soon after, but McGrory saw his cross-shot come back off the bar and Michael Carville equalised for the visitors on the stroke of half-time, finishing from close range after good work by Peter Thompson and Andrew Waterworth.
The Blues took control of the contest when McGrory fouled Michael Gault inside the area in the 49th minute, and Waterworth dispatched the resulting penalty.
Phillip Lowry added a third as David Jeffey's side made it six consecutive wins to move a point clear at the top of the table.
Linfield's cause was helped by Portadown's inability to beat newly-promoted Warrenpoint Town, and it could have been even worse for Ronnie McFall's side, who found themselves 2-0 down after 36 minutes at Stangmore Park.
Daniel Hughes continued his rich vein of scoring form with a goal after seven minutes, before Tony Devlin sprung the Ports offside trap and rounded keeper David Miskelly to score his side's second.
Portadown found a way back into the contest in the second half, with Peter McMahon equalising in the 40th minute before Darren Murray tapped in a Chris Casement cross in the 69th minute to rescue a point for his side.
In the game at Seaview, second half goals from Jordan Owens and Paul Heatley consigned defending champions Cliftonville to their fourth defeat of the season.
Heatley struck first for the Crues with a great solo effort, slaloming his way through the heart of the Reds' defence before dispatching his shot past Conor Devlin in the 60th minute.
It took just a minute for the hosts to double their advantage, with Declan Caddell's cross finding Owens who rose unmarked inside the area to power a header past Devlin.
The afternoon got worse for the Reds stopper soon after when he was shown a straight red card following an off-the-ball incident involving Caddell. The defeat means Tommy Breslin's side drop to fifth in the table, with Crusaders moving up to fourth.
In the game at the Coleraine Showgrounds, Coleraine were 2-1 winners over Ards to secure their third win of the season.
Ruairi Harkin's penalty set the Bannsiders on their way in the 54th minute, before Shane Jennings smashed home a 67th minute volley from inside the area after Gary Brown's knockdown.
Ards fought their way back into the game and grabbed a goal when Paul McDowell pounced on a Wayne Drummond error in the 73rd minute to set up a frantic finale.
In spite of their best efforts though, the visitors couldn't find another goal and Coleraine clung on for the victory.
Finally in the game at the Oval Glentoran were 2-1 winners over Dungannon Swifts.
Marcus Kane headed in the opener for Eddie Patterson's side after seven minutes, but Jamie Douglas found the net for the visitors with a header of his own in the 17th minute.
Mark Miskimmin put the hosts back in front with another headed goal, this time from a Jason Hill cross, and Hill had a chance to make it 3-1 from the penalty spot soon after, but his effort was brilliantly saved by Gareth Buchanan.
However the Swifts could not muster a further reply, as Glentoran held on to bring their four game winless streak to an end.
Meanwhile on Friday night, Ballinamallard United secured the three points in their fixture against Ballymena United with a goal from Ryan Campbell sealing a 1-0 victory.
Results in full:
Cliftonville 0-2 Crusaders
Crusaders: Heatley 60, Owens 61.
Coleraine 2-1 Ards
Coleraine: Harkin 54 (PEN), Jennings 67.
Ards: McDowell 73.
Glenavon 1-3 Linfield
Glenavon: Bates 22.
Linfield: Carvill 40, Waterworth pen 49, Lowry 53.
Glentoran 2-1 Dungannon Swifts
Glentoran: Kane 9, Miskimmin 54.
Dungannon Swifts: Douglas 17
Warrenpoint Town 2-2 Portadown
Warrenpoint Town: Hughes 7, Devlin 36.
Portadown: McMahon 40, Murray 69.
Ballinamallard United 1-0 Ballymena United (04/10/13)
Ballinamallard Utd: Ryan Campbell 60