Gill top scored with 64 not out, while Weeks chimed in with a handy 57 before being caught.
Not huge totals, but the runs came off 46 and 38 balls respectively.
CD reached 175 for the loss of four wickets after 21.2 overs to claim the match by six wickets.
CD coach Dilan Raj praised the actions of the Whanganui lads and Hawkes Bay skipper for leading the side to a win.
"Akash and Connor made sure we stayed in the game by limiting runs at the start - they had great games," Raj said.
"And Akash and Kurtis did an outstanding job with the bat. Looking at the balls they faced showed they ran Canterbury ragged."
CD had two draws in the two day action with Wellington taking first innings points in the first match and. CD then claimed first innings points against Northern Districts before a rest day on Tuesday.
CD were playing Wellington again yesterday, this time in the one day format although the result was unavailable at press time.