Half-time substitute Kretzschmar took just five minutes to open his account, drilling past Scott Flinders from 20 yards, and he added a fine second 18 minutes later when he calmly slotted home Matt McClure's fine through ball.
Wanderers weren't at their best in the first half, but the ,much-improved second half display got what it deserved, despite James Poole scoring an injury-time consolation.
Gareth Ainsworth made three changes to the side that beat Exeter 2-0 on Tuesday with Leon Johnson, Gary Doherty and Steven Craig recalled to the starting line-up.
Anthony Stewart, Max Kretzschmar and Jo Kuffour were the men to make way and they were named amongst just six substitutes.
Dean Morgan was absent through illness, while Matt Bloomfield was suffering from a tight groin following two appearances in four days.
Josh Scowen’s ankle injury had not cleared in time and Jon-Paul Pittman continued to nurse a slight back problem. Charles Dunne served the final match of a three-game ban.
Matt McClure and Craig both saw early efforts from inside the area blocked as Wanderers started brightly.
However, the hosts had the best two chances early on when Simon Walton headed a corner wide, before Andy Monkhouse’s goalbound shot was superbly blocked by Doherty after Luke James had nodded back across goal.
United gradually took a stranglehold of the half and Jonathan Franks wasted a great chance to give the home side the lead when he drilled wide from close-range following Matty Dolan’s lofted cross to the far post.
Hartlepool came even closer in the 26th minute when Wanderers failed to deal with a corner and Monkhouse’s close-range effort looked destined to find the back of the net until Nick Arnold threw himself in the way to clear off the line.
Billy Knott’s free-kick clipped the top of the wall before being cleared and that was the closest the Blues came in the opening half an hour.
A clearer chance came 10 minutes later though when McClure’s strong challenge found Wood on the left and the winger’s dangerous cross was just in front of Craig, who would have had a tap-in.
Ainsworth made his first change at the break with Kretzschmar replacing Arnold and they started well with Lewis’ strike deflecting wide.
Blues’ best chance came from the resulting corner when McClure rose above his marker but headed Kretzschmar’s set-piece wide.
Wanderers’ improved play was rewarded three minutes later.
Kretzschmar, who had made such a difference to the Chairboys’ display, ran on to a clever knock down from McClure and steadied himself before drilling low into the far corner from 20 yards.
It was the 19-year-old’s first professional goal and he reached that milestone in some style before celebrating with Ainsworth and Richard Dobson.
Flinders kept the hosts in the game in the 67th minute when he dived full length to his left to parry away Lewis’ 20-yard strike.
However, the lead was doubled less than 60 seconds later.
The impressive Wood and McClure combined to find Kretzschmar, and the 19-year-old’s first touch was perfect and took him into the area where he coolly slotted into the bottom corner, giving no Flinders no chance.
Hartlepool pushed forward in search of a lifeline and Dolan curled a free-kick over the wall, but just past the post with eight minutes remaining.
Ainsworth made his final chance four minutes later with Stewart replacing Craig and the centre-back was utilised in a holding midfield role to add protection to the back four.
Ingram made a comfortable save from Monkhouse before the winger then dragged wide from just inside the area.
It could have been three in the 89th minute when Kretzschmar dispossessed Austin near the corner flag and the ball fell to Kuffour who burst into the box and cut back for Knott, only for the midfielder to fire wide under pressure
Poole set up a grandstand finish in the second minute of injury-time, heading home at the far post, but the Wanderers saw out time to record the victory built on a fine second-half display..
Wanderers: Ingram, McCoy, Hause, Doherty, Johnson, Arnold (Kretzschmar 46), Lewis (c), Knott, Wood, Craig (Stewart 86), McClure (Kuffour 76).
Subs: Harrison, Fletcher, Spring.
Hartlepool: Flinders, Duckworth, Baldwin, Burgess, Austin, Franks (Poole 64), Walker (Walton 7), Dolan, Compton (Howard 79), Monkhouse, James.
Subs: Rafferty, Collins, Richards, Rodney, Howard.
Attendance: 3,640 (120)