The right hander, who has looked in decent touch all season without going on to make a score, made light of the blustery conditions and put the Langtons bowling to the sword with a boundary-laden knock, which came from just 118 balls, helping his side to post a mammoth 379 for 7 from their 50 overs.
Buck hit 12 fours and ten maximums as he bettered the previous best in the Premier League by eight runs - a record previously held by current skipper Dave Torr, who made 153 against Thorpe Arnold in 2014.
Despite passing his landmark, Torr was delighted with his opener: "I'm extremely pleased and proud of him - records are there to be broken," said Torr. "It was a special knock - knowing when to rotate (the strike) and hit boundaries. The weather conditions were probably the worst to play cricket in and to perform like that shows the class of him."
Liam Kinch made 80 from 68 and shared in a stand of 160 with Buck to take Sileby from 162 for 2 to 322. Kinch's departure five runs later checked the momentum and put pay to any chances of reaching the 400 mark.
Aaron Smith, who has started the season brilliantly with the ball, ripped out four Langtons wickets early on to finish with 4-39 while Ryan Dawson picked up his third Premier League 5-fer to clear up the middle order and tail, finishing with 5-45 from his ten overs.
Vijal Vinay top scored with 72 for the home side, being one of three victims behind the stumps for Josh Winterton, and also took 3-65 with the ball for the home side as they fell 171 short of Sileby's target on 207 - having asked the visitors to bat first.
Sileby host Cropston at Mill Lane next weekend.