Tshimanga opened the scoring from the penalty spot on 23 minutes after Ollie Harfield was sent off for deliberate handball.
The striker doubled the lead just before half-time with a tap-in before completing his treble as the game approached the hour-mark.
Saidou Khan got the Spireites’ fourth of the afternoon in what was a dominant performance from start to finish.
Here are Liam Norcliffe’s player ratings from the game...
1. Scott Loach 6
His eighth clean sheet - and easiest - of the season. He could have got a deckchair out as Weymouth failed to have a shot on target and their only attempt in the whole game came in the 90th minute. Photo: Tina Jenner
2. Tyrone Williams 7
A solid debut from the new signing. Started ahead of Kerr on the right of the back three and didn't put a foot wrong. Took up a position higher up the pitch in the second-half and brought a save out of Fitzsimons with a close-range header. Photo: Tina Jenner
3. Jamie Grimes 7
Back in the side after being suspended last week. He stamped his authority on the game with two bullet defensive headers from Leslie-Smith's long throws. There were some crossfield passes out from the back as well. It was a good performance from him and they will need him to stay fit now Gunning and Maguire are injured. Photo: Tina Jenner
4. Luke Croll 7
An impressive display on his first league start after making his debut in the FA Cup last week. He started on the left of the three-man defence - his prefrerred position - and he slotted in as if he had been playing there for Town for a long time. He joined in attacks and there were some silky bits of skill and play from him. Photo: Tina Jenner