After scoring only 27 points in the first half, the Hawkeyes' offense awoke after halftime with a 12-5 run sparked by Smith's putback of his own misfire.
Smith and Haluska sealed the win by scoring 27 of Iowa's last 30 points.
Poor shooting by both teams kept the score low early in the game as Cornell (4-7) took a 10-3 lead thanks to a pair of 3-pointers by senior Graham Dow.
Iowa (8-6), which entered play shooting a Big Ten-worst 43.7 percent, made just two shots in the game's first 10 minutes.
Cornell wasn't any better, earning just two free throw attempts and shooting 33.3 percent in the first half.
But the Hawkeyes awoke with eight minutes left in the first half when Haluska sank consecutive 3-pointers from the left corner to tie the game at 15. J.R. Angle followed with two free throws to give Iowa its first lead of the game. The Hawkeyes went into intermission up by four.
Brian Kreefer added a 3-pointer of his own to tie the game at 29, but the Big Red never regained the lead.
Mike Henderson set an alley-oop to Smith -- one of two for the freshman in the second half -- with 7:15 left for a 47-40 lead that marked the beginning of the end for Cornell.
On Iowa's next possession, Smith hung in the air and flipped the ball off the glass with his left hand, drawing a foul in the process. He made the free throw to put the Hawkeyes up by double digits.
Wittman led Cornell with 13 points and Kreefer added 10.