THE Linnets came through a nervy game following a first half brace from Joe Francis on his return to the side after injury.
Francis became the first wide player to score more than 20 league goals in a season for the club.
Francis is the ninth player to do the feat (the last being his teammate Danny Bloomfield), but all the previous players have been centre-forwards.
Lynn boss Keith Webb said: "We played particularly well in the first half. We kept our shape and passed the ball around well.
"Our front four caused them no end of problems. At half-time we were forceful with the team – there was no pat on the back.
"We knew the next goal would be important. Fisky with his enthusiasm gave away a sloppy free-kick which got a deflection.
"Then we and the crowd got nervous, which is understandable, but we hung in there.
"At this time of the season it's three valuable points.
"They probably didn't have the necessary quality to hurt us at the back.
"Joe Francis took his goals well. He did well with the header and he gives us balance.
"I've got to look at what we do at half-time, it seemed to drag on. Their keeper didn't have a second-half save to make, which was disappointing."
The first chance of the game fell on seven minutes to Lynn's Matt Nolan, who turned and shot over from 12 yards.
Brackley had a glorious opportunity, but Danny Spencer blazed over from close range following a corner.
Brackley committed a handball a yard inside their box, but the referee gave it a yard outside, and Francis was unlucky to see his curling free-kick hit the upright.
Francis made amends a minute later (the 27th) from an almost identical position, this time rolling the ball under the wall in a moment of Ronaldo-esque skill and cheek.
Francis completed his double five minutes later with a looping header at the far post from a cross by Nolan, who just before the interval fired inches past the post.
The lead was fully deserved by half-time, but afterwards Lynn's cohesion broke down.
Both sides were well wide with efforts from outside the box before a 25-yard free-kick by Brackley sub Tom Winters squirmed under keeper Scott Howie's gloves on 65 minutes.
Howie emerged from a shaky spell by saving from Spencer's free-kick as Lynn endured some nervous moments.
The pressure eased when full-back Phil Murphy was sent off for his second yellow card three minutes from time for a push on breakaway sub Michael Frew.
Lynn: Howie, West, Bains, Crane, Chapman, Turner (Frew 64), Fisk, Sedgemore, Francis (Melton 78), J. Defty, Nolan. Subs (not used): Bloomfield, C. Defty, Murray. Booking: Chapman. Goals: Francis (27, 32).
Brackley: Knight, Abbassi, Murphy, Hadland, Brown, Oldfield (Patterson 90), Harper, Savage, Spencer, Fisher (Winters 54), Anderson. Subs (not used): Willshere, Green, Longford. Booking: Murphy. Sending off: Murphy. Goal: Winters (66).
Referee: R. Beevor (Norfolk). Attendance: 1,265.
Stats, Lynn first: shots on target 3, 4; off target 7, 5; corners 7, 4; offside 1, 5; free-kicks 14, 14.
MoM: Joe Francis.