Jessica Kuster scored 16 points and Megan Palmer compiled 15 points for Rice (1-1).
Summitt, who led the Lady Vols to eight national titles in 38 seasons, stepped down in April after announcing last year she has early-onset dementia. She watched Thursday's game from a midcourt seat as the Lady Vols delivered the type of dominant performance they produced so often during her tenure.
The Lady Vols (2-1) have recorded two straight one-sided victories since getting stunned 80-71 at Chattanooga last week in the head coaching debut of Holly Warlick, who served as Summitt's assistant for 27 seasons.
Warlick said after the game that she asked for ball pressure from the point guard to allow the four players behind her to jump passing lanes, and Ariel Massengale, Andraya Carter and Meighan Simmons delivered in their stints on top of the floor on the defensive end.
The result was 32 points for Tennessee off 22 Rice turnovers. A close game midway through the first half became a blowout as Tennessee went on a 72-19 run.
Harrison set career highs in points and rebounds with her double-double of 16 and 12.