The former Gunners striker (pictured) notched twice after the half-time interval to secure a third victory in four games against Arsenal so far this campaign.
Blues named an unchanged line-up from the side that had defeated Chelsea three days earlier, but Karen Carney took up a more central role with Remi Allen shifting to the right-hand side of midfield.
The visitors had the better of the opening exchanges and had the first clear sight on goal in the 14th minute. After a sustained spell of possession in the Arsenal half, Jo Potter spun on the ball and curled a precise right-footed pass in behind left-back Emma Mitchell which picked out the marauding Chelsea Weston - but she could not repeat her scoring feat from the weekend and fired wide.
A minute later, centre-back Leah Williamson tried to play out from defence but only succeeded in picking out Linnett who forced Emma Byrne into a full-stretch save with a curling effort from the edge of the area.
An end-to-end first half was epitomised in the 20th minute when Carney was released down the left flank – she cut inside and fired an effort which was blocked by Alex Scott and Arsenal countered with Freda Ayisi who skipped past Potter before firing wide.
A matter of inches separated Linnett and the lead in the 34th minute. Carney’s right-wing corner picked out her England international teammate Jade Moore but her header just avoided Linnett, who was trying to turn it home on the spin from six yards out.
One minute later there was a sense of déjà vu for Blues when Moore whipped in a ball from the right which picked out Allen in the centre of the box and, in a style reminiscent of the Champions League first leg, the midfielder tried to cushion an effort towards the far post with her right foot - but history did not repeat itself as Byrne dived at full stretch to palm the effort away.
Blues had their biggest scare of the half with seven minutes to go when Mitchell’s cross almost deceived Rebecca Spencer in the Blues goal but, fortunately for Blues, she fumbled the effort wide for a corner. In the aftermath, she made amends by claiming the resultant corner with real authority – taking a heavy blow in the process.
Four minutes later, she was in action again as she tipped over Smith’s dipping effort to ensure the scores were level at half-time.
Three minutes after the restart, Blues had the goal they deserved. Williamson again attempted to play out from the back, but only succeeded in picking out Linnett, who showed fantastic composure to round Byrne and slot into the empty net.
Not content, Blues were pressing for a second goal and thought they had it when Allen poked home after Linnett’s through ball - but the midfielder was rightly adjudged to have been offside.
A superb last-ditch Weston tackle denied the lively Ayisi and it was the right-back who would, on the hour mark, prove the catalyst for Blues’ second goal.
A fantastic block tackle on Ayisi resulted in Carney picking up possession – she turned and slipped the ball to Allen who in turn played a perfectly-timed through ball to Linnett and the striker confidently poked past Byrne for her fourth goal of the campaign.
Despite the Gunners pressing for a route back into the game, Blues were still looking for a third goal and felt aggrieved not to have a penalty when Linnett’s curled effort clearly struck an Arsenal hand – but referee Joshua Smith waved away the appeals.
A last minute 25-yard strike from Smith was as good as it got for the hosts as Blues kept their third clean sheet of the season against Shelley Kerr’s side and they sit pretty at the summit with a trip to champions Liverpool awaiting on Saturday.
Blues Ladies: Spencer; Weston, Mannion, Harrop, Carter; Moore, Potter; Carney (Simpkins, 88), Allen, Lawley; Linnett (Keryakoplis, 88).
Subs not used: Baggaley, Sargeant, Westwood, Wilkinson, Torkildsen.
Goals: Linnett (48, 60)
Arsenal Ladies: Byrne, Scott, Mitchell, Kinga (Murray, 74), Stoney, Ohno, Carter, Smith, Williamson, Ayisi (Weir, 81), Bailey (Yankey, 63)
Subs not used: Chamberlain, Hoogendijk, Fahey, Humphrey.