The teams remained at the top of Group D with four points, although Real Salt Lake has the advantage on goal difference. Still, it was a missed opportunity for both clubs as the winner would have clinched a spot in the round of 16 with a victory.
Instead, the match lacked excitement and scoring chances, and was the second match of the tournament to finish in a scoreless draw.
The best scoring chance for either side came in the closing seconds of first-half stoppage time when Minnesota's quick counter-attack finished with Robin Lod's left-footed shot that beat RSL goalkeeper Zac MacMath, but rattled off the post.
Lod had another opportunity early in the second half but MacMath got his hand on the shot. Real Salt Lake nearly got a late winner only to watch Sam Johnson's shot in the 87th minute pulled just wide of the goal.
MacMath finished with three saves and Minnesota goalkeeper Tyler Miller had two.
Real Salt Lake (1-0-3) lost some of its offensive attack when Albert Rusnak was helped off the field in the first half with a left leg injury. Rusnak scored RSL's first goal of the tournament in its opening victory over Colorado.
Minnesota (3-0-1) knocked off Sporting Kansas City 2-1 in its opener.
Real Salt Lake will close the tournament against Sporting KC, and Minnesota will finish against Colorado. Both matches are next Wednesday.