Town's strong away form continued as Weaver's men won all three points down in Sussex.
Three first half goals from Martin, March and Power put the travelling side in a strong position but an early second half goal for Crawley and a Will Smith red card made the final 20 minutes a tough battle.
Simon Weaver made one change to the team that beat Newport County last weekend, with Connor Hall returning from suspension to partner Will Smith at the back.
The homeside meanwhile, handed a league debut to 34-year-old Mark Wright, who is more well known for his role in British TV series 'The Only Way Is Essex'.
The first chance of the afternoon came within the first five minutes, with Irshiman Simon Power getting forward and earning Town an early corner.
Thomson’s delivery made its way to Aaron Martin, with his header forcing a reasonably comfortable save for Glenn Morris in the Crawley goal.
That chance was a sign of things to come and eight minutes later, Town got the breakthrough. A nice interchange of passes from frontmen Josh March and Martin resulted in space for the latter inside the box.
Martin neatly knocked the ball past his marker and finished well past Morris, making it goals in back to back games for the striker.
Town were finding joy down the right throughout the first half with Power exposing the relatively inexperienced Mark Wright at left back.
However, Town’s second of the afternoon would come from the opposite flank. Josh McPake started a Town counter attack and burst at pace at the Crawley defence.
It left them stretched and the winger did well to pick out March at the perfect moment, allowing the striker to push into the box and win a penalty after Luke Wright had no choice but to bring the attacker down.
March stood up to take the penalty and placed it into the bottom left corner to make it three goals in three games for the striker as the 30th minute passed.
Crawley failed to test Belshaw throughout the first half with their closest sight at goal being an effort high and wide from midfielder Sam Matthews.
As the half came to an end, it was Town who finished in the ascendency, adding a third in injury time. Man of the half, Power, picked up the ball outside the Crawley box and being under no pressure, decided to take aim.
The strike took a deflection on it’s way towards Morris’ goal but the keeper could do nothing to stop Power scoring his first Town goal.
Crawley made three substitutions during the interval with Mark Wright, Ashley Nadesan and Jack Powell all making way.
However, it was Town who started the half more brightly with March stinging the palms of Morris with a fierce strike.
Crawley were looking more dangerous though, and a cross from the left was well cleared by Burrell who was making his 250th appearance in a Town shirt.
The Red Devils did then bring themselves back into the contest as Tom Dallison smashed home a loose ball which came from a Crawley corner.
Belshaw had done superbly to make a great double save but could do nothing with the third attempt.
It gave Crawley confidence with Josh Wright next to have an attempt. This time it was no trouble to Belshaw.
Town would then make it a testing final 20 odd minutes after Will Smith brought down Ashley Nadesan in the 67th minute when the midfielder looked to go clean through on goal.
The defender was shown a straight red card and the resulting free-kick saw the Crawley bench think they had scored to reduce the deficit to one, only to realise the ball had dropped the otherside of the net.
Weaver made the change to bring Jake Lawlor on for McPake, with Lloyd Kerry and Jack Muldoon following soon after.
Credit must go to Weaver’s men who put in an incredible shift after going down to 10 men.
Josh Andrew’s made his debut in the final few minutes of the match, coming on for a fatigued Aaron Martin who had run his feet into the ground.
The three points at The People’s Pension Stadium moves Town to 14th in the league, six places higher than at 3pm on the same day.
Crawley Town: Morris, Francomb, McNerny, Powell (Allarkahia 46), Nadesan (Maguire-Drew 46) Nichols, Matthews (Frost, 76), Craig, M Wright (Dallison 46), Hessenthaler (Davies 76), J Wright.
Subs not used: Galach, Nelson.
Goals: Dallinson 53'
Yellow Cards: J Wright, Nichols
Town: Belshaw, Burrell, Smith, Hall, Francis, Power (Kerry 73), Falkingham, Thomson, McPake (Lawlor 70'), March (Muldoon 73), Martin.
Subs not used: Minter, Kiernan, Andrews
Goals: Martin 13', March 30', Power 45'
Yellow Cards: McPake
Red Cards: Smith
Referee: Dean Whitestone