The Linnets move up to sixth place following their best away win since the beginning of last season at Team Bath, which saw the same scoreline.
It was arguably their finest display on their travels since the 4-1 effort at Histon in January 2004 which set up Lynn's title-winning campaign.
On Tuesday the team shrugged off their weekend defeat and were simply irresistible, and if not for home keeper Richard Wilmot's heroics the goals would have been approaching double figures.
Lynn boss Tommy Taylor said: "We played the 90 minutes in their half of the field."
Paul Kelly and Matt O'Halloran came in for injured midfielders Mark Camm and Dean West respectively.
In the first quarter-hour the Canaries were pinned back as the visitors enjoyed six corners and had six attempts on goal.
Winger O'Halloran, who was outstanding, crossed for skipper Jack Defty to direct a downward header which Wilmot saved with his legs, Wilmot doing the same with an effort from Cedric Anselin.
In between, Wilmot also denied Martin McNeil and Sam McMahon from corners, and Defty with his feet.
But from the resulting corner, McMahon centred and Danny Bloomfield gave Lynn the lead on 16 minutes with a bullet-header.
The hosts had a better spell between 20 to 30 minutes but only looked like scoring when Josh Sozzo hit the bar on 27 minutes, swiftly followed by Adam Jones almost notching an own goal, clearing a cross to hit his own post.
Wilmot finished the half with a tremendous diving save to thwart Anselin.
However, Defty doubled the lead on 53 minutes with another powerful header after great work by Bloomfield and a cross from the right by O'Halloran.
Bloomfield became the Premier Division's leading scorer (with seven goals) ten minutes later with a turn-and-shot which went in off both posts when Anselin and Adam Smith combined on the left.
O'Halloran got the goal he deserved ten minutes from the end, smashing home with his right foot that gave Wilmot no chance when Jack Defty held the ball up and laid it off.
James Bunn came on and bagged his first goal for Lynn on 85 minutes, hitting home a penalty after he was fouled by Wilmot.
Near the end McNeil was blatantly elbowed by the half-way line, which went unnoticed by the officials, while John Higgs saved well from sub Stuart Lochhead's free-kick.
Bloomfield and Smith were excellent, Smith never giving pacy Danny French a look-in.
Taylor added: "Matt kept out wide like I wanted. Their full-back couldn't afford to go out and mark him, it would have left the centre-forwards on their own.
"Young Smithy was excellent, Paul Kelly came in and did the things he can do.
"The four in midfield were excellent while Jack and Blooms up front did their job, and we played some good balls into them."
Hitchin: Wilmot, Lamacraft, Duffy, Cretton, Ayres, McMenamin (Lochhead 55), French, Mills (Jenner 55), Sozzo, Hayes, Pugh (Bridge 55). Subs not used: McCulloch, Ducket.
Lynn: Higgs, Smith, Jones, McMahon, Cooper, McNeil, J. Defty, Anselin, Kelly (C. Defty 87), Bloomfield (Bunn 80), O'Halloran. Not used: Harris, Hammond, Benstead. Booked: McNeil (47, foul); O'Halloran (89, dissent).
Att:223. Referee: C. Francis (Ely).