Trey Stross had 91 yards receiving and a touchdown for the Hawkeyes, who rallied from a 14-point deficit for the second straight week to win their third game in four tries.
With home games against Minnesota and Western Michigan remaining, Iowa (5-5, 3-4 Big Ten) needs just one more win to become bowl eligible.
The Wildcats, meanwhile, blew a chance of becoming bowl eligible for the second straight week. Northwestern led Purdue 17-14 after three quarters last week, but was outscored 21-0 in the fourth quarter.
Northwestern led 17-14 after three quarters yet again against Iowa, but was outscored 14-0 in the fourth this time.
Christensen's 53-yard pass to Stross down the left sideline set up a 2-yard touchdown run by Sims with 7:44 left, giving Iowa its first lead of the game, 21-17.
Northwestern (5-5, 2-4) had two chances to put it away, but C.J. Bacher threw interceptions on consecutive possessions -- one to Bradley Fletcher and the other to Charles Godfrey.
Godfrey's interception with 5:08 left led to Sims' second score, an 8-yard run that gave Iowa a 28-17 lead.
Bacher threw for 264 yards, a touchdown and three interceptions for the Wildcats. Tyrell Sutton added 116 yards rushing and a score.
The Hawkeyes trailed 14-0 after the first quarter -- getting outgained 196-11 -- but outscored Northwestern 28-3 the rest of the way to snap a two-game losing streak to the Wildcats.
After managing just 12 yards and no first downs in the first quarter, Iowa finally got a first down with 12:42 left in the second when Sherrick McManis was penalized for roughing the kicker on a Hawkeyes punt.
Iowa then scored for the first time late in the quarter, pulling within seven on Christensen's 20-yard touchdown pass to Stross with 49 seconds left.
Adrian Clayborn blocked a 34-yard Northwestern field-goal attempt in the closing seconds of the second quarter to keep the score 14-7.
Iowa then opened the second quarter with a 71-yard, 10-play drive to tie it at 14. Albert Young capped the drive with a 16-yard score, taking the handoff up the middle, juking toward a hole on the right and running untouched into the end zone.