Paul put the Lightning ahead 2-1 at 4:47 of the second period when he beat Hintz to the puck and scored from the slot.
"We were pushing through the middle, winning second battles, coming out of the corners and getting looks," Paul said. "When you get pucks to the net and are winning battles, things open up."
Pavelski tied it 2-2 at 8:02 with a power-play goal on a follow-up shot from in front.
Robertson gave Dallas a 3-2 lead at 9:57 with a shot from the slot off a pass from Pavelski.
"It was one of our closer games, most of our wins have been by a lot," Roberson said. "It's our second game of the year in overtime. We had a lot of chances in overtime, but you can't get beaten up the ice."