This was a result and performance to forget for Slough, who fell behind on 6 minutes. Mitford showed good composure to latch on to a through ball and slide the ball past Luke Williams.
Slough failed to respond and Burnham doubled their lead on 28 minutes, Mitford again on hand to prod home a cross following good work down the right from Kane Jones.
A minute before the interval, Mitford completed his treble as he side-footed in a volley from a cross.
Slough looked hungrier and brighter in the second half, with Callum Webb putting a shot straight at Burnham keeper Ouhla and sending another over the bar.
However, their threat fizzled out and Burnham spurned a chance to score a fourth in the dying minutes. John Bennett was felled in the penalty, but Williams saved the resulting spot-kick, moving to his left to deny Carl Davies.
Burnham Line up
Zaki Ouhla, James Walters, Dom Rhone, Lewis Fogarty, Carl Davies (c), Justin Clayton, Kane Jones, Kensley Moloney, John Bennett, Tre Mitford, Josh Millar. Subs: Mahamood Kadi, Shaun Downes, Andy Forisky.