David McCracken looked to have rescued a point for the home side with a second-half strike after they had fallen behind to an earlier effort from Thompson.
That goal came after 30 minutes when Thompson's long-range effort squeezed past Wycombe keeper Jamie Young, who should have done better but could only parry it into the net.
Just before the break Wanderers came close to an equaliser when Lee Sawyer flicked the ball up on the edge of the Magpies box and hit a dipping volley just over the bar.
Shortly after half-time the Chairboys got their equaliser when skipper McCracken ventured forward and slotted home after being picked out in the box by Gary Holt.
Wycombe were very edgy in the closing stages as County applied pressure and they lost the precious point when Thompson curled a superb effort in from distance.