Bird hit 5 of 7 3-pointers for Seattle (1-3) after she had made just 5 of 17 in the first three games of the season. Bird and Little and had seven points each as the Storm outscored Tulsa 21-11 in the third quarter to break open a close game.
Seattle increased its lead to 57-46 after three quarters as the Shock made only 2 of 17 from the field in the quarter.
Jennifer Lacy scored 12 points and fellow reserve Riquna Williams had 11 to lead Tulsa (0-5), which has lost 11 straight dating to last season when it finished 3-31.
Seattle avoided matching its worst start since its inaugural 2000 season.