The Hawkeyes (23-12) reached the quarterfinals, where they will take on the survivor of Sunday's contest between Virginia and St. John's.
Stony Brook surprised Massachusetts in the first round of the tournament and played Iowa to a standoff through the early moments of the second half.
The Hawkeyes took the lead for good on a 3-pointer by Mike Gesell with 16:07 to play and moved in front from there. Aaron White added 13 points for Iowa.
Stony Brook (25-8) was paced by Jameel Warney with 17 points.