Woodrow - who only made his Reds debut on November 3 - fired the hosts into an early lead from the spot and sealed victory with a clinical second on 64 minutes as Daniel Stendel's second-placed side put some daylight between themselves and automatic promotion rivals Portsmouth and Sunderland.
In the process, Barnsley also claimed a spot of revenge following a 1-0 loss at Wycombe on December 8, with the Chairboys being the last team to beat them in the league.
The early evidence suggested that Wycombe, who had taken a point on their travels at Portsmouth and Sunderland and won at Bradford City, might pose a problem or two, just as they did in the reverse fixture at Adams Park.
Fortunately, the hosts were handed a soothing opener to further enhance confidence levels and the palpable feel-good factor at Oakwell, with a familiar source taking the plaudits on 13 minutes.
That said, Wycombe were aghast when referee Matthew Donohue pointed to the spot after Mike Bahre, making his first league start since December 29, tumbled under pressure from Luke Bolton, who was adamant that his challenge was a legitimate one.
Woodrow avoided the controversy to stroke home his third goal in two matches and ninth in 15 starts for the Reds.
The Reds controlled the tempo of the game and produced some nice passing movements, with Wanderers keeper Ryan Allsop doing well to claw away a well-struck long-ranger from Dani Pinillos, which was destined for the top corner after taking a deflection.
But on 40 minutes, the hosts were indebted to a fine save at the other end from captain Adam Davies, who blocked a point-blank effort from Luke Freeman following a dangerous centre from former Reds defender Jason McCarthy.
At the other end, the hosts spurned a glorious chance to take in a 2-0 lead in at the break when Alex Mowatt found himself clear in the box, but he failed to crown his birthday week with Allsop blocking his effort.
After starting the game with intent, Wycombe produced a carbon copy on the restart and conjured a good opportunity from a well-worked corner routine, with Bolton firing straight at Davies after being teed up by Alex Samuel.
Bolton's eventful afternoon then took a turn for the worse after he was received lengthy attention after suffering a bad fall, which saw a number of medical staff on the pitch.
Thankfully, Bolton was able to walk off the pitch following several minutes of treatment to the nearby dressing room, while looking in some distress.
Once play resumed, Barnsley promptly put the game to bed, thanks to the predatory radar of Woodrow.
The striker emphatically fired into the roof of the net from close range four minutes after the hour mark following good build-up play by substitute Ryan Hedges and Jacob Brown.
The hosts started to turn on the style with McGeehan seeing a curler flash just wide before Brown went close twice, while Wycombe saw appeals for a penalty rebuffed following Pinnock's challenge on substitute Nathan Tyson.
Woodrow went close to his hat-trick when Allsop tipped his header over following Mowatt's corner before Liam Lindsay headed over from the resultant flag-kick.
A minimim of ten minutes of stoppage-time arrived following the lengthy attention for Bolton, with Wycombe's misery compounded in a fractious finish when captain Adam El-Abd was dismissed after appearing to pull the hair of McGeehan.
They did grab a late consolation when Joe Jacobsen netted from the spot after Pinnock brought down sub Scott Kashket.
Barnsley: Davies; Cavare, Pinnock, Lindsay, Pinillos; Mowatt (Dougall 87), McGeehan, Bahre (Adeboyejo 86); Thiam (Hedges 63), Woodrow, Brown. Substitutes unused: Walton, Green, Jackson, Styles.
Wycombe: Allsop; McCarthy, Jombati, El-Abd, Jacobsen; Bolton (Tyson 61), Gape, Thompson, Freeman (Akinfenwa 67); Cowan-Hall (Kashket 67), Samuel. Substitutes unused: Yates, Stewart, Bean, Bloomfield.
Attendance: 11,824 (411 Wycombe supporters).