Chasing Trinidad's 148 for nine, Ballance (64 off 37) and Rashid (33 off 27) lifted Yorkshire from a difficult position with an unbeaten 103-run partnership fifth wicket partnership.
Ballance struck as many as six sixes and two fours while Rashid decorated his innings with three hits to the fence and one over it.
Ravi Rampaul and Samuel Badree returned with identical figures of one for 22 for the Caribbean outfit.
With two wins from as many games, Yorkshire stormed into the main draw of the tournament from Pool 2. Trinidad, unfortunately, have crashed out of the event after just one outing, which means their final match againsr Uva becomes inconsequential.
Earlier, Denesh Ramdin led from the front with a scintillating half-century while Darren Bravo scored a vital 45 to help Trinidad and Tobago post a competitive 148 for nine.
Ramdin scored 59 off 40 deliveries, while Bravo's 45 came off 49 balls as they combined beautifully to rescue Trinidad from a precarious position with a 93-run fourth wicket partnership.
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Chasing 149 for win, Yorkshire did not have the best of the starts as they slumped to 51 four by the ninth over.
Openers Phil Jacques (6) and skipper Andrew Gale (2) failed to provide any significant contribution for the English outfit and perished in consecutive overs.
Joe Root (16) and Adam Lyth (18) both got starts but failed to capitalise on them and became victims of Yannick Ottley and Rayad Emrit, leaving Yorkshire's chase in disarray at 51 for four.
But if the Caribbean players thought they had a grip over the match, they were in for a rude shock as Gary Ballance and Adil Rashid had other plans.