Tshimanga pounced from close-range after just five minutes and added another from the penalty spot shortly after. The striker completed his treble with a second spot-kick after the break.
Gavin Gunning’s deflected free-kick wrapped up the points after the Bees had come back from two-nil down to level.
Here are Liam Norcliffe’s player ratings from the game...
5. Jeff King 7
A bit hit-and-miss at times but overall he had a big influence on the game. His corner delivery led to Chesterfield's first goal and his driving run into the box drew a foul for Tshimanga to make it 3-2 from the spot. Almost scored himself late on but Sargeant made a top save from his header. Photo: Tina Jenner
6. Curtis Weston 7
The midfielder had a particularly good second-half, snapping into tackles and breaking up play to stop Barnet from countering. He plays that role so well. He has been suffering with a sickness bug and he limped off with 10 minutes remaining due to tightness. Photo: Tina Jenner
7. Manny Oyeleke 7
Bossed the midfield area, particularly during Chesterfield's explosive start. A few errors creeped in but overall he did well. Photo: Tina Jenner
8. Calvin Miller 7
A hard-working performance down the left flank. Came close to an assist in the first-half when his cross from the left was scooped over the bar by Tshimanga. Replaced by Whittle with 15 to go. Photo: Tina Jenner