Andraz Kirm looked to have earned the hosts a point in the 54th minute when he cancelled out Andreas Johansson's opener.
However, the visitors had other ideas, Utaka tapping home Hans Henrik Andreasen's 80th-minute free-kick and then Jensen putting the result beyond doubt in stoppage time.
Utaka could have got his name on the scoresheet as early as the 10th minute, but sent his header wide when well placed.
Andreas Johansson also had a decent chance for the Danish side in the early stages but he too failed to find the target from close range.
Neither goalkeeper was seriously tested until the 34th minute, when Wisla stopper Sergei Pareiko parried Utaka's shot around the post.
Pareiko was beaten moments later, though, when Johansson latched onto Chris Sorensen's pass and found the bottom-right corner from 12 yards.
Gervasio Nunez drilled a 25-yard free-kick wide in the 36th minute for Wisla, but the hosts had to wait until after the interval for the equaliser to arrive.
They started the second half strongly with Kew Jaliens firing wide and Dudu Biton just off target with a header, but the home fans had something to cheer about in the 54th minute when Kirm latched onto Maor Melikson's pass from the left and found the bottom-right corner with his shot.
Kirm could have doubled his tally two minutes later but lashed just wide from the edge of the box.
Johansson also had the chance to bag his second goal of the night just before the hour, but he managed to send his effort over the bar from close range.
Odense goalkeeper Stefan Wessels did well to keep his side on level terms just after the hour when he tipped a Dudu Biton blast around the post.
That save proved crucial when the Danish side forged ahead in the 80th minute, Utaka converting Andreasen's free-kick, and then Jensen put the icing on the cake by prodding home Baye Djiby Fall's pass in stoppage time.