Platt headed United into a 40th minute lead which was doubled by Knowles in first half stoppage time.
Platt and Knowles both added further second half efforts and the icing was applied to United's cake by skipper Luke Shiels three minutes from time.
It was the perfect riposte to the Pilgrims’ 3-0 reversal at Gloucester City on Saturday, who had made three changes ahead of kick-off, with Jordan Adebayo-Smith handed a full debut.
United bossed the opening stages and carved out the game’s first meaningful opportunity when Nicky Walker crossed from the right and Knowles was only denied his first Boston goal by a fine Tony Thompson save.
Adebayo-Smith fired two efforts off target as the Pilgrims continued to press but they eventually took the lead five minutes before half-time.
Walker delivered a deep corner to the back post and PLATT steered home a powerful close-range header.
KNOWLES doubled United’s lead two minutes into added time when he played in Adebayo-Smith to cross from the right before getting on the end of the resulting centre to break his duck in front of goal for the Pilgrims.
Simon Ainge produced a terrific block to keep out Jordan Hulme at the beginning of the second half during a brief Altrincham renaissance but the Pilgrims soon put the game to bed.
PLATT swept home United’s third goal in the 63rd minute with a crisp finish from 20 yards and subsequently turned provider to slip KNOWLES in to finish with eight minutes to play.
Platt was at the heart of things again when he headed down Walker’s deep corner for SHIELS to stab home his first United goal with three minutes remaining.
Boston (4-3-3): Peter Crook; Karl Byrne, Luke Shiels, Simon Ainge, Alex Whittle (Ashley Jackson 76); Brad Abbott, Andi Thanoj, Tom Platt; Nicky Walker, Dominic Knowles (Tom Clare 85), Jordan Adebayo-Smith (Shaun Tuton 68). Subs (not used): George Green, George Willis (gk).
Altrincham (4-2-3-1): Tony Thompson; Shaun Densmore, James Jones, Toby Mullarkey, Connor Hampson; Sean Williams, Conor Branson (Jake Moult 71); John Johnston (Lewis Walters 69), Max Harrop (Simon Richman 46), Ashley Hemmings; Jordan Hulme. Subs (not used): Andy White, Tom Peers.
Referee: Jon Kenny.
Attendance: 1,143 (55 visitors).