With time running out, Minnesota's Mats Zuccarello dug the puck out of a scrum on the side boards and slipped a pass to Dumba in the slot. The Wild defenseman made a move and flipped a wrist shot past Calvin Peterson with 0.3 seconds left.
"Eyes in the back of his head," Dumba said of Zuccarello's unexpected pass. "I don't know how he saw me through all those guys."
Joel Eriksson Ek, Nico Sturm and Kirill Kaprizov also scored for the Wild. Kaapo Kahkonen made 25 saves as the Wild won their sixth straight.
Drew Doughty, Austin Wagner and Adrian Kempe scored for the Kings, who overcame a three-goal deficit to force overtime. Peterson stopped 38 of 42 shots for Los Angeles.
After giving up three early goals in a 3-1 loss to Minnesota on Friday night, the Kings came out with much more energy and dominated the pace of play early, outshooting Minnesota 9-3 at the start.
But, just as they did on Friday, the Wild struck quickly and jumped out to a 3-0 lead.
"We were disappointed we got into that hole again, but the team stuck with it and clawed their way back in right to the last second," Kings coach Todd McLellan said. "It's a good sign for our group. It's not a good sign that we're falling behind right now. ... In any case, we probably earned a point tonight and lost two, so got what we likely deserve."
Eriksson Ek took advantage of a bit of luck to put the Wild on the board first at 14:17 of the first period. After entering the zone on a give-and-go, Kevin Fiala took a one-handed whack at the puck and tapped it toward the slot.
The puck bounced to Eriksson Ek, who chipped it puck over Peterson's shoulder for his team-leading eighth goal of the season.
Three minutes later, the Wild doubled their lead on an impressive individual effort by center Nick Bjugstad. While holding off defenseman Tobias Bjornfot, Bjugstad controlled the puck as he circled behind the net.
Bjugstad then fired a backhand pass across the face of the goal, finding Sturm alone at the far post for an easy tap-in.
Kaprizov made it 3-0 early in the second period when he took advantage of another fortunate bounce for the Wild. Victor Rask broke his stick on a slap shot, but the puck trickled right to Kaprizov in the slot, and he fired it home for his sixth of the year.
Doughty began the Los Angeles comeback less than two minutes later with a power-play goal. Kempe took a blast from the left point that Kahkonen kicked out to his right, but Doughty flicked the rebound into the open net for his fifth of the year.
Wagner drew the Kings closer with an unassisted goal midway through the second. He blocked a shot near the blue line and had a clean breakaway, which he converted with a wrist shot off Kahkonen's blocker, cutting Minnesota's lead to 3-2.
Kempe tied the game when he scored from the point with 2:45 to play in the third. It came on the Kings' third consecutive power play of the third period.
In overtime, Peterson stopped Kaprizov on a breakaway and the Kings killed off a two-minute power play just before Dumba's last-second heroics.
"We felt we had good enough chances to win the game," Kempe said. "I think we took over in the second and the third period and they had some bounces going their way."
OVER AND ABOVE IN OT
Saturday's game wrapped up the season series between the Wild and Kings, with Minnesota winning five of the seven meetings. Three of Minnesota's victories came in overtime. All three ended 4-3.
It's all part of a trend for the Wild, who are 4-0 in overtime and haven't gone to a shootout this season.
"We aren't just looking to shoot or set up," Minnesota coach Dean Evason said of the team's overtime approach. "We are hanging on to some pucks and moving and making people try to take it off us. We play fast in the overtime. We play quick, and I think that's probably helped us in that area."
After two weeks on the road, the Kings return to Los Angeles for a game against the Coyotes on Wednesday.
The Wild head back out on the road for the first of two games at Vegas on Monday.
Dumba beats OT buzzer to hand Wild a dramatic win
Mats Zuccarello finds Matt Dumba out in front, who scores just before overtime ends to propel the Wild past the Kings.