The high-scoring Lanarkshire outfit moved second top of the Central First Division standings, nine points adrift of the Nock with a game in hand, but Sinky put a bit of perspective on their latest victory.
"We didn't have a single failure on Saturday, with the front pairing of Ross McGeachie and Graham Gracie particularly outstanding, however we cannot allow ourselves to get too excited.
"We came into the game on the back of a 4-3 defeat by Lanark last week so it's all about finding consistency between now and the end of the season.
"This is a very difficult league where everyone barring East Kilbride Thistle is capable of beating one another and many more displays like that are going to be needed if we want to stay in the promotion running."
Jags weathered early pressure to get their noses in front around the 20th minute thanks to Mark Canning's cool finish into the corner of the net.
The goalscorer then turned provider with a great run and cross that allowed McGeachie to volley home to make the half-time scoreline 2-0.
A decisive moment occurred shortly after the restart when Greenock were awarded a penalty kick, however Larkie goalkeeper Davie McEwan foiled Ross Kearns with a superb double save.
The home side were left to rue that miss as Alan Fleming's powerful header found the net to put the visitors 3-0 ahead.
Prolific hitman Gracie exploited the spaces left by Greenock going for broke with two goals over the closing stages to seal a stunning triumph.
Losing gaffer Stevie Mooney said: "Larkhall are definitely our bogey team as that's twice they have turned us over this season by big scores and on each occasion the lad Gracie has given us a torrid time.
"He's a class act but this was no one-man show because truth is Larkhall were better than us all over the pitch and we can have few complaints about how things panned out."
The only Second Division encounter to beat the big freeze saw Maryhill go back atop the table with a resounding 4-1 defeat of third-placed Rossvale at New Petershill Park.
Barry Jones, Paul Callender, Ally Murray and Craig Ferguson were the marksmen as Brian Heron's young side leapfrogged previous front-runners Cambuslang Rangers.
Changes, too, at the Super First Division sharp end after Largs Thistle moved top of the pile with a 3-2 victory over Ardossan Winton Rovers at Barrfields.
Willie McClure with a double and a Kevin Struthers penalty accounted for the Largs goals while Graeme Hamilton bagged a brace for basement battlers Rovers.
Yet another top versus bottom Super First affair saw title- challenging Kilbirnie Ladeside falter at struggling Whitletts Vics through a 2-2 share of the spoils at Dam Park.
Indeed, it took a penalty kick conversion by Mark Archdeacon to deny rank bottom markers Whitletts all three points after they led 2-1 against the 10-man Blasties (Darren McLean sent off for two bookings) going into the closing stages.
Archdeacon had opened the scoring with a fourth-minute rising shot following a corner kick for the visitors, who were then rocked as a superb Mark Cameron 25-yarder and Neil McGinn close-range header gave the Vics a 2-1 half-time lead.
Several clubs arranged friendlies on artificial pitches as scores of matches were postponed due to the freezing weather.
Bellshill Athletic had a notable 3-1 triumph over Emirates Cup holders Shotts Bon Accord, while Rutherglen Glencairn lost out by the same scoreline to Lanark United. Arthurlie overcame a youthful Albion Rovers 2-0.