But the emphatic 6-0 win did come at a cost, adding three more players to the injury list ahead of an important week of matches in league and cup.
Melton made the two-hour round trip to Northamptonshire with a skeleton squad depleted by injury and holidays and then lost player-manager Tom Manship, captain Leon Fray and Price.
Despite Raunds’ struggles this season, they had sacked their manager in the preceding week, bringing some of last season’s successful players back, and Manship reminded the team to not take anything likely.
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Melton came out of the traps quickly and took and early lead for the third game running.
The ball was won in midfield and a through ball split the Raunds defence, finding Sam Thorpe who slipped a shot under the oncoming keeper inside two minutes.
Raunds should have levelled from their first corner when Ben Page was found unmarked with a clear view of goal, but he fluffed his shot.
Melton dominated possession, while Raunds relied on breakaways which brought the better chances.
Midway through the half Dalitso was played through as the defence appealed for offside, but the officials waved play on and Peet had to save low down to prevent an equaliser.
Minutes later the same player was allowed to turn in the area and send a thunderous shot inches wide.
Town started to use Tom Rigby and Joe Lindley on the flanks much more and this turned the game on its head with three goals in 14 minutes before half-time to put the game beyond the hosts.
Josh Burniston, making his league debut, sent Thorpe away with a superb pinpoint pass, and his pace took him clear to round the keeper before he was crudely chopped down.
The resulting penalty was clinically converted by Parsons for the second straight game.
Minutes later a throw-in found Reeve who cut in from the edge of the box and sent a powerful low shot into the far corner of the net.
Lindley then found Thorpe with a cross from the left and the forward thumped a header past the keeper to make it 4-0 at half-time.
Only 10 second-half minutes had elapsed when Melton made it 5-0.
Burniston’s great ball through the statuesque defence teed up Reeve who slotted his second under the keeper.
Melton then lost their intensity as Tom Manship and captain Leon Fray went off injured, the latter with a groin strain.
Having used up their first substitute, and with Price injured in the warm-up, Melton were left with 10 men for the final 15 minutes.
But the man advantage was not evident as Melton continued to create chances.
A corner was poorly cleared to Rigby whose first-time shot clipped the bar before Hill’s free-kick found Reeve at the far post whose header was kept out by the keeper.
But with the final kick of the match Reeve claimed his hat-trick.
Receiving the ball midway in the Raunds half, he drove at the defence and his shot on the run beat the keeper for power to burst the roof of the net.
The win kept Melton top of Division One ahead of Saturday’s crunch meeting with second-placed Lutterworth Town, who are also unbeaten, at Melton Sports Village (ko 3pm).
Before that, they travel to Stamford to take on Blackstones in the league cup on Wednesday (ko 7.45pm).
Town: Peet, Rigby, Lindley, Manship, Fray (Leon), Hibbitt, Hill, Burniston, Reeve, Thorpe, Parsons. Sub: Reek.