Jackson, the league's reigning MVP, suffered a poor shooting night but finished with a team-high 14 points to go with six rebounds and two steals.
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The Australia captain's shooting mirrored that of her new-look team in a poor opening half, but a 23-1 run to end the third quarter ended the contest.
"In the second half, we just got into the flow and showed some pretty great things," Jackson, who had just two points at half-time , said.
"When our defence breaks down, it generally takes a toll on our offence. If we get it right defensively, good things will come."
The Storm rebuilt in the off-season to be an intimidating team as they chase a second championship.
As well as Jackson and Sue Bird, they now boast former league MVPs Sheryl Swoopes and Yolanda Griffith as well as All-Star Swin Cash - every one an Olympian.
In other games on opening day, Tully Bevilaqua made a successful start for Australians in the American league, scoring eight points in Indiana's 64-53 triumph over Washington.
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Katie Douglas scored 24 points in her Indiana debut, while Nakia Sanford finished with 14 points and 11 rebounds for the Mystics.
In Phoenix, No.1 draft pick Candace Parker scored 34 points - the most in a WNBA debut - and added 12 rebounds to help Los Angeles beat the Mercury, the defending champions, 99-94.
In Auburn Hills, Michigan, Katie Smith scored 21 points and Plenette Pierson added 17 to help Detroit cruise past Houston 85-66.
Alexis Hornbuckle, the No.4 draft pick by the Shock, had eight points and set a franchise record with seven steals less than two months after helping Tennessee win the NCAA championship.
Tina Thompson led Houston with 17 points and Mwadi Mabika and rookie Matee Ajavon added 12 each.
In Connecticut, Tamika Whitmore had 22 points and 10 rebounds to lead the Sun past Atlanta, the newest franchise in the WNBA, 100-67.
Asjha Jones added 18 points, Barbara Turner 15 and Lindsay Whalen 11 for the Sun, who scored 100 points in regulation for the second time in franchise history.
Betty Lennox led Atlanta with 17 points.