The duo were on target at Damson Park as Mark Thompson's side opened their league campaign with a maximum three-point haul.
Harris opened the scoring and Melson scored the winner after Solihull had equalised.
Boston (3-4-2-1): Charlie Wilkinson; Taylor Jaine, Owen Sheriff, Ben Robson; Elliot Foster, Ben Johnson, Finlay Armond, Zane Millar; Han Stevens, Charlie Earth; Sam Harris. Subs (used): Krisztian Gagyi, Joe Melson, Jake Henderson, Logan Tate; (unusued): Mackenzie Burdass.
Referee: Adrian Bancroft.
PIC: Russell Dossett.