The Chairboys winger opened the scoring on 53 minutes, driving the ball into the top corner of the net from the edge of the box.
With Barnet pressing for an equaliser, Wycombe doubled their lead late in the game.
Thompson won and converted a penalty in the 90th minute, after being brought down in the box by Bira Dembele.
Barnet had chances in the first half, with John Akinde almost putting the Bees ahead after seven minutes.
A pass from Bondz N’Gala found Akinde one-on-one with Matt Ingram in the Wycombe goal, but he pulled his shot wide of the far post.
The Bees had two further chances as they approached the half time break.
In the 43rd minute Luke Gambin’s shot rattled off the crossbar, following a Barnet corner.
Then a minute later Akinde charged into the penalty area, only to see his shot go wide of the far post.
Following Thompson’s second half goal, Michael Gash went closest to levelling things up for the Bees.
The substitute’s bicycle kick was cleared off the line in the 84th minute, with Wycombe’s Pierre clearing the ball to safety.
Ultimately though it was the Chairboys who found the net in the closing stages, doubling their lead with a couple of minutes left on the clock.
Barnet return to league action on Tuesday when they face Northampton Town at The Hive.
BARNET: Stack, Hoyte (Tomlinson 57'), N'Gala, Dembele, Johnson, Yiadom, Togwell, Champion, Gambin (Batt 69'), Weston (Gash 57'), Akinde.
Subs not used: Stephens, Muggleton, Nelson, Vilhete.