Lynn's Matt O'Halloran struck a brace as The Walks outfit stretched their unbeaten league and cup run to eight games on Tuesday.
O'Halloran was on target once in each half as Lynn moved into the top five for the first time since early August.
Manager Tommy Taylor said: "I didn't think Cirencester were as good as they were last season, but we still had to beat them.
"We had to deal with a few crosses into our box and Higgsy has been called upon to make one good save, but other than that they didn't really trouble us.
"As a team we played well and looked solid at the back.
"We missed a couple of good chances before we actually scored. Matt could have had a hat-trick by the end of the night."
Taylor kept faith with the same starting line-up as the one which beat Northwood with a solitary Adam Smith goal on Saturday.
Lynn born-and-bred Jack Defty made his 150th appearance in a Linnets shirt, but his milestone was curtailed after he received a knock to the head in the final 20 minutes of the game.
Struggling Cirencester held the upper hand in the early stages with a succession of crosses into the Linnets' penalty area.
But The Walks outfit began to find their feet and Adam Jones blazed over after a fine run which took him to the edge of the Cirencester box.
And it was Heath-Preston who carved out the chance of a third goal late on, but his pass fell short of the waiting Bloomfield.
O'Halloran went close with a long-range effort before a Jones centre was cut out in front of the same player.
But Lynn didn't have to wait long to break the deadlock when a long pass found O'Halloran in space.
O'Halloran slid the ball to Jones, before heading the return past Thompson in the home goal in the 31st minute.
Two minutes later the busy Danny Bloomfield surged down the right, but his dangerous centre was cleared for a corner.
Bloomfield repeated the dose soon after with Jones the recipient, but the defender completely missed his kick in front of the target.
Cirencester bossed the early stages of the second half, without troubling Higgs.
The game was effectively ended as a contest 12 minutes after the restart when the
persistence of Bloomfield led to him squaring the ball for O'Halloran to fire home his second.
Lynn's second settled any nerves, allowing them to play some neat football from the back. Defender Grant Cooper was at his best, setting a fine example to the remainder of his rearguard.
Taylor replaced the injured Defty with Danny Hammond and hero O'Halloran made way for Mark Heath-Preston.
Lynn: Higgs, Smith, Cooper, West, Jones, , McMahon, Camm, Anselin , Bloomfield, Defty (Hammond
O'Halloran (Heath-Preston 78). Subs not used: Fell and McNeil.
Cirencester: Thompson, Arndale , Fullam, Jackson, Horgan, Viveash,
Robison, Smith (Musgrove 45), Hopkins, Danks, Cowe.
Referee: Mr J Holbrook (Kidderminster) Attendance: 171