This one-sided affair started so well for the visitors, who took the lead with less than half a minute played, but Slough took little time to turn it around and then raced to a 5-1 half time lead.
Just like at Stratford the previous Saturday, Slough lacked concentration from the off, and Jordan Nicholson's strike from around 25 yards seemed to catch Mark Scott off guard before nestling in the bottom corner.
The Cambridgeshire side's joy was very short-lived as less than four minutes later, Slough levelled with Putman's first competitive goal for the club. He swept the ball through the legs of Histon keeper Denzel Gerrar after strong work from Nathan Webb on the left of midfield, beating Ryan Auger to play the ball across.
Adam Martin's well-struck volley flew wide before Nathan Webb produced a good save from Gerrar, the keeper diving to turn the ball away as Webb tried to curl it into the far corner.
Slough took the lead on 23 minutes. Ryan Parsons' deep cross was flicked on by Scott Harris and struck at goal by Warren Harris. The ball deflected off a defender and off a post, with Putman able to bundle home his second of the match from inside the six yard box.
Nathan Webb went close to setting up another for Scott Harris, but played the ball just too far in front of the striker. Webb was forced off with an injury soon after and was replaced by his brother Callum.
The Rebels hit a further three goals in the space of nine minutes before half time to put the game beyond Histon.
On 36 minutes, Scott Harris blasted through the hands of Gerrar after Evan Key's weak clearance fell straight to him. Warren Harris was heavily involved with an industrious run and low cross from the right.
Four minutes later, Harris pounced to score his second, volleying in superbly after Gary MacDonald nodded down a long throw from Guy Hollis in a crowded penalty area.
Slough cut through the Histon defence with ease, and Putman was denied a first half hat-trick by the foot of Gerrar, the keeper doing well to save after the striker was put clean through on goal by a ball over the top of the defence.
A minute before the interval, Adam Martin picked the ball up on the edge of the box after a corner was cleared, before shifting the ball superbly onto his left foot – beating three defenders in the process – and firing in a shot which took a wicked deflection off Key and into the roof of the helpless Gerrar's goal.
Histon started the second half positively without really threatening Scott's goal, Ryan Auger having a long-distance strike held easily.
Martin clipped a delicious ball over for Callum Webb to chase on to, but he was unable to beat Gerrar.
Slough notched a sixth goal on 62 minutes, Scott Harris completing his treble. A superb team move down the left involving a one-two between Callum Webb and Lewis Putman led to the latter playing his strike partner through, with Jack Uttridge playing him well onside, and Harris made no mistake, poking the ball into the net. The striker has now scored three hat-tricks in a Rebels jersey, the first also coming in a 7-1 win at North Greenford last year.
The rampant Rebels went close on several occasions to scoring a seventh goal, Warren Harris seeing a shot blocked and Putman firing into the side netting.
With five minutes left, Putman completed his own treble to round off the scoring. His run took him past Danny Rumens and Elkanah Simbanda and he was allowed space to get in a low shot which slipped past Gerrar and into the corner.
Histon Line up
Denzel Gerrar, Rogan McGeorge, Jack Uttridge (Elkanah Sibanda 68), Evan Key, Danny Rumens, Ryan Auger, Lee Smith, Tom McGowan (Salim Relizani 63), Sam Ives, Curtis Fulcher (Nick Freeman 63), Jordan Nicholson. Subs not used: Brendan Brown, Matthew Meacher.