Katie Gearlds came off the bench to score a career-high 17 for the Storm, who shot 44% (30 of 68) from the field and improved to 3-0 all-time in the series against the Sky.
Seattle has won two straight games since its three-game losing streak.
Trailing 35-33 in the second half, Seattle took control for good behind an impressive 14-6 burst to close out the third quarter.
The Storm pulled away in the fourth quarter as Jackson, Gearlds and Betty Lennox combined for all the points during an 18-6 run with 5:03 remaining to make it 77-56.
Candice Dupree scored 18 points and Armintie Price had career highs with 17 and 13 rebounds for Chicago, who shot 38% (26 of 68) from the field.
In Tuesday's other match, Shameka Christon - who was replaced by Ashley Battle in the starting line-up - scored 16 points and grabbed six rebounds to lead the
New York Liberty to a 79-69 win over the winless Washington Mystics.
Reserves Janel McCarville had 11 points on four-for-four shooting and Barbara Farris had 10 points for the Liberty, who snapped a two-game losing streak.
Catherine Kraayeveld scored 11 points for the Liberty, who shot 42% (26 of 62) from the field.
Washington were led by DeLisha Milton-Jones, who had 20 points and nine rebounds.
Alana Beard scored 17 points and Monique Currie added 12 for Washington, who shot just 34% (21 of 61) in its eighth straight loss.