Wanderers took the lead in the fifth minute when Max Kretzschmar's effort fell kindly to Beavon and last season's top scorer beat his man before placing a low effort into the far corner from just inside the area.
The hosts drew level eight minutes later when Farnborough striker Phil Page finished at the second attempt after Gary Doherty had superbly cleared an initial effort off the line.
Beavon restored the Chairboys' lead in the 24th minute as he latched on to a loose ball and burst past a defender before exquisitely chipping Farnborough keeper Craig Bradshaw from the edge of the area.
Joel Grant grew into the half as it wore on and he forced Bradshaw to tip over an effort before crossing for Kretzschmar who headed straight at the keeper.
Matt McClure almost added a third five minutes before the break, but his header from Grant's cross was well kept out by a diving Bradshaw.
Blues finished the half firmly in control and were carving through their hosts with a number of quick passing moves.
Boss Gary Waddock made eight changes at the break with only Matt Ingram, Charles Dunne and Anthony Stewart coming out for the second half.
The changes made for a disjointed start to the second half, but Dunne came close with a 25-yard effort that just cleared the bar.
Farnborough's Solbas Jean-Michar then had a tame effort easily saved by Ingram, who had little to do up until that point.
Emmanuel Ighorae almost claimed a fortunate third 15 minutes from time when a Farnborough defender clattered a clearance into him, but the ball drifted just wide.
Midfielder Stuart Lewis had the final chance of the game with five minutes remaining, but he shot just over from 20 yards.
Wycombe first half: Ingram, Stewart, Dunne, Hause, Doherty, Grant, Kewley-Graham, Spring, Kretzschmar, Beavon, McClure.
Second half: Ingram, Stewart, Dunne, Winfield, Johnson, Ighorae, Lewis, Scowen, Wood, Triallist, Logan (Kewley-Graham 72).
Farnborough: Bradshaw, Smith, Treacher, Bosch, Inns (c), Bygrave, Bennett, Laidler,Page, Moody, Tarpey.
Subs: Jefrries, Lye, Jean-Micher, Knight, Quarm, Orlu, Bent, Lawal, Crossley.