Kretzschmar finished coolly inside seven minutes before Wood avoided the need for a nervy ending when he headed home at the end of a smart move to leave the Blues on 40 points at the mid-point of the season.
Gareth Ainsworth opted to freshen up his side for the second match in three days, making four changes and resting experienced quartet Paul Hayes, Garry Thompson, Joe Jacobson and Matt Bloomfield.
Kick-off was delayed by seven minutes after the Reds’ team coach was stuck in traffic and they started slowly, almost conceding within two minutes when Stephen McGinn’s goalbound shot crashed into Aaron Amadi-Holloway and bounced clear.
At the other end, Sonny Bradley headed harmlessly over from a corner, but the Reds were caught cold when Aaron Pierre’s forward pass found the defence flat-footed and Max Kretzschmar held off his man before slotting home calmly for his third goal of the season.
Chances began to dry up after a lively start, but Crawley found themselves in some promising positions only to be lacking a finishing touch, while Wanderers’ defence did what was required to keep them at bay.
Michael Harriman’s powerful low drive was blocked en route to the bottom corner before Mitch Hancox was inches away from making contact with Gwion Edwards’ inviting cross to the near post.
Sam Wood came close to doubling the lead shortly before half-time when the keeper and Lewis Young hesitated and Wood nicked in to loft the ball goalwards, only for Jon Ashton to hook it behind for a corner on the goal-line. From the resulting delivery, Anthony Stewart was close to making contact to a loose ball after Amadi-Holloway had returned it into the danger zone.
There were no changes at the interval and the start of the second period followed a similar theme with Crawley always looking like they were still in the game, but without testing Matt Ingram.
Amadi-Holloway forced a save from Callum Preston when he glanced Sam Wood’s cross towards goal, before Aaron Pierre was called into action with two brave blocks in quick succession, firstly denying Gwion Edwards following great play by Roarie Deacon, and then diverting Lee Barnard’s crisp drive behind.
Michael Harriman was just unable to convert a deep cross by Stephen McGinn before Ainsworth introduced Paul Hayes and Garry Thompson from the bench in a bid to find a crucial second goal to tie up the points, and their presence gave the hosts an extra dimension with a series of half-chances presenting themselves. Luke O’Nien was denied by the keeper from a Sam Wood cross before Aaron Pierre rose above Preston and Thompson was just robbed of a shooting chance by the recovering defender.
Wycombe were dealt a blow when Hayes came off injured with five minutes remaining, presenting Brentford loanee Jermaine Udumaga with his Chairboys debut, and man-of-the-match Sam Wood almost clinched the points in the closing stages when he flew in to meet Michael Harriman’s cross but saw the ball bounce agonisingly wide.
However, he wasn't to be denied his goal, and it came inside the first of six minutes of stoppage time when Udumaga teed up Garry Thompson, whose floated cross found Wood unmarked and he headed home in front of the terrace to make it a perfect Christmas.
Wycombe: Ingram, McCarthy, Jombati, Stewart, Pierre, Harriman, O’Nien, McGinn, Wood, Amadi-Holloway (Hayes 69 (Udumaga 86)), Kretzschmar (Thompson 69).
Unused subs: Lynch, Rowe, Sellers, Ugwu.
Crawley: Preston, Young, Hancox, Bradley (Harrold 67), Yorwerth, Ashton, Smith, Walton, Edwards, Barnard, Deacon (Fenelon 83).
Unused subs: Flahavan, Emmanuel, Jenkins, Rooney, Tomlin.
Attendance: 4,153 (232 from Crawley)
Winning 50/50 Draw Number (Blue £1): 0450
Prize Money: £758.50
Winning 50/50 Draw Number (Orange £2): 2501
Prize Money: £54.00