Iowa (16-9, 5-7 Big Ten) led by at least 10 twice in the game but couldn't put away the league's last-place team until late.
The Nittany Lions (8-16, 0-12) went 0 for 2 from the field in the last 30 seconds with a chance to tie or take the lead, capped by Basabe's block of Jermaine Marshall's drive to the paint.
Marble was fouled on the ensuing inbounds and hit two foul shots for a four-point lead with 20.9 seconds left.
Penn State had one last chance, down three with 1.5 seconds left and Marshall on the foul line. Marshall hit both shots, but the Nittany Lions whiffed on a chance for a game-tying putback if Marshall had missed at the line.
Penn State wasted an inspiring effort from lead guard D.J. Newbill, who finished with 26 points on 11-of-20 shooting and eight rebounds. Marshall added 10 assists and finished with 14 points, but went just 3 of 13 from the field.
The Hawkeyes broke a four-game conference road losing streak and won their first game in Happy Valley since 2006.
They nearly let it slip away late.
But Marble and Masabe were able to help Iowa hold on down the frantic stretch. Basebe finished with 11 points, six rebounds and four blocks.
Sasa Borovnjak's three-point play drew the Nittany Lions within 70-67 with 1:55 left before a foul shot by Marshall cut the lead to two.
With the game on the line, the Hawkeyes put the ball in the hands of Marble, who scored 14 after halftime. The junior let the shot clock wind down to 10 on a late possession but lost the ball on the drive to the basket.
Still, Penn State couldn't convert in transition after Newbill missed a 3 with 35 seconds left.
Penn State clawed back from two double-digit deficits, the last one down the stretch with the help of scrappy play by two unheralded walk-ons seeing more time of late. Kevin Montminy hit a 3 before 6-foot-9 forward Alan Wisniewski had a block and helped force Iowa into a shot-clock violation in a 7-0 run that got the Nittany Lions within 62-59 with 6:29 left.
The Nittany Lions went 8 of 17 from 3-point territory, a season-high in conference play, but lost the rebounding edge 40-29.
Borovnjak added 14 points for Penn State, which was forced to look for other options much of the second half with Newbill facing an array of double teams and defensive switches.
The lower-division Big Ten teams traded scoring spurts in a chippy and entertaining first half that ended with Aaron White hitting a 3 from the corner before the halftime buzzer to give the Hawkeyes a 38-34 lead.
Led by Newbill's inspired play, the Nittany Lions went on a 16-0 run midway through the first half to take a 23-17 lead before the Hawkeyes regrouped after a timeout and responded with a 9-0 run. Freshman Mike Gesell had 10 points on 4-of-6 shooting in the half, surpassing his season average (8.8 points) in his first 17 minutes on the floor.
Gesell finished with 13 on the night.