It took just three minutes for the Reds to find the net, with Liam Boyce finishing from close range after Chris Curran's cross.
Boyce then turned provider for Cliftonville's second, beating the Glens defence before teeing Martin Donnelly to smash up a low drive past Elliot Morris in first half stoppage time.
Mark Miskimmin gave Eddie Patterson's side hope when he fired high into the net after his initial effort had been saved by Conor Devlin, but Boyce dispatched a penalty in the 73rd minute after Stephen Garrett had been fouled by Jamie McGovern.
Joe Gormely added a fourth, five minutes later when he capitalised on poor positioning by Morris in the Glentoran goal to wrap up a convincing win for Tommy Breslin's side.
In the game at Windsor Park, Ballymena United manager Glen Ferguson saw his side come unstuck against his former employers Linfield, with Andy Waterworth scoring a hat-trick in what was a 4-1 victory for the blues.
Waterworth's first came via a 10th minute header, and the former Glentoran striker added a second when he latched on to Michael Carville's weighted pass nine minutes later to make it 2-0.
Gary Liggett gave the Sky Blues hope when he netted from a Michael McLellan flick-on soon after the restart, but Linfield's two-goal lead was restored when Waterworth cvonverted from the spot to complete his hat-trick after he was fouled by Dwayne Nelson.
The Ballymena players were incensed by the decision, with captain Allan Jenkins shown a straight red for dissent in the immediate aftermath of the incident.
Rodney Brown opened his account for the blues with a fourth goal in injury-time to seal a victory which sees David Jeffrey's side move up to third in the table.
The 4-1 score line was a running theme in Saturday's matches, with Glenavon also scoring four in their game against Ards at Mourneview Park.
Scott Davidson netted the opener for Ards with a second minute penalty, but after that it was all Glenavon.
Guy Bates levelled with a spot-kick of his own in the 10th minute, and David Rainey made it 2-1 25 minutes in when he capitalised on a good pass from Andy McGrory.
McGrory got himself on the scoresheet in the 71st minute when he reacted quickest after Rainey's shot struck both the post and Ards keeper Graeme McKibben, and Andy Hunter's late own goal sealed the win for Gary Hamilton's side.
In the game at Shamrock Park Portadown couldn't quite follow their record-breaking 11-0 win over Ballinamallard with a similar scoreline on Saturday, managing just two goals in their 2-1 victory over Dungannon Swifts.
It took Darren Murray less than a minute to find the net with a fine effort into the top-corner after a mistake by Richard Copeland, and Kevin Braniff added a seconds with a fierce shot from just outside the area after half an hour.
Dungannon pulled one back when Jamie Douglas netted from David McCullough's cross five minutes later, but that was as good as it got for the visitors, as Portadown wasted a host of chances to extend their lead in the second half but ultimately held on for the win.
Ballinamallard, meanwhile, bounced back from their drubbing at the hands of Ronnie McFall's side by securing a 2-1 win away to Coleraine.
All the goals came in the last seven minutes, with Andy Crawford netting the opener for the Mallards in the 83rd minute, collecting a long ball upfield before rounding Wayne Drummond in the host's goal.
Crawford added a second five minutes later after being set up by Jason McCartney, who had earlier seen his first-half penalty saved by Drummond.
Derry GAA star Eoin Bradley came on for his Coleraine debut and added a consolation goal for the Bannsiders in the dying moments.
Finally in the game at Stangmore Park, Crusaders needed a last-gasp equaliser to salvage a point against Warrenpoint Town.
Daniel Hughes put the hosts in front with a header in the 49th minute, but Josh Robinson nodded home a Paul Heatley corner a minute into stoppage time to snatch a point for Stephen Baxter's side.
Results in Full:
Glenavon 4-1 Ards
Glenavon: Bates 9 (PEN), Rainey 25, McGrory 71, Hunter og 75.
ARDS: Davidson 4 (PEN).
Cliftonville 4-1 Glentoran
Cliftonville: Boyce 3, (PEN) 73, Donnelly 45+1, Gormley 78.
Glentoran: Miskimmin 66.
Coleraine 1-2 Ballinamallard United
Coleraine: Bradley 90+1.
Ballinmallard: Crawford 83, 88
Linfield 4-1 Ballymena United
Linfield: Waterworth 10, 19, (PEN) 60, Brown 90+1.
Ballymena: Liggett 51; Jenkins sent off 62.
Portadown 2-1 Dungannon Swifts
Portadown: Murray 1, Braniff 31.
Dungannon: Douglas 36.
Warrenpoint Town 1-1 Crusaders
Warrenpoint: Hughes 49.
Crusaders: Robinson 90+1.