Co-hosts the United States seemed under pressure when Canada made 5-194 batting first and then lost a wicket to the second ball of their innings.
The total demanded the United States achieve their highest-ever run chase in a T20 international to win the match, eclipsing the previous best of 169.
In the end they reached the target with ease and with 14 balls remaining courtesy of Jones' 10th six.
It had all looked very different when captain Monank Patel departed in the seventh over, as they slipped to 2-66.
But Jones, who had been out of form in recent matches and came into the match with a strike rate of 100, hit the fastest T20 half-century for the US from 22 balls and at a strike rate of 227.
At least two of his blows carried more than 100 metres and would have been home runs at Grand Prarie Stadium in its previous incarnation as a baseball stadium.
Jones turned the match with a superb innings that pushed the pressure firmly back on Canada.
That showed when Jeremy Gordon bowled an 11-ball 14th over which went for 33 runs.
Jones put on 131 runs in a match-winning partnership for the third wicket with Andres Gous who made 65 from 46 balls with seven fours and three sixes.
 South Africa-born Gous was out just before the end, as chants of "USA, USA'" echoed around the stadium..
Tournament co-hosts the West Indies begin their campaign on Sunday (Monday AEST) with a match against Papua New Guinea in Guyana, while Oman play Namibia in Barbados.
Australia's opening game is against Oman on Wednesday in Barbados.
