Manny Fernandez made 39 saves and Pascal Dupuis answered a late Pittsburgh rally with a power-play goal for the Wild, who were outscored, 12-3, in losing the first three games of a four-game road trip.
Robert Lang and Jan Hrdina scored for the Penguins, who have dropped back-to-back games after a season-high four-game unbeaten streak.
Zholtok scored twice in a 3:45 span of the second period to give the Wild a 2-0 lead.
On the first score, Marian Gaborik slide a pass across the ice to Zholtok, who guided the puck into the net from in front of the right circle.
With Andrew Frerence off for crosschecking, the Wild capitalized minutes later with Zholtok scoring his seventh goal of the season. Zholtok took a cross-ice pass in the left circle from Richard Park before easily beating Johan Hedberg.
Lang cut the lead in half with a power play goal with 1:34 left in the period. Lang, who was added to the Czech Olympic team on Thursday, converted on a rebound after Fernandez made a save on Kris Beech.
An exceptional effort by Gaborik increased the lead to 3-1. Gaborik tried to skate between defenseman Michal Rozsival and Josef Melichar before losing control of the puck. He finally recovered it before being Hedberg from in close.
Hrdina scored on a power play with 5:01 left to cut the lead to 3-2, but Dupuis answered 36 seconds later when he worked the puck away from defenseman Darius Kasparaitis and beat Hedberg from in close.
Wes Walz capped the scoring with a shorthanded empty-net goal with 35 seconds left.