Mikheyev made it 2-0 at 18:22 with a wrist shot from above the left face-off circle that beat Soderblom between the pads with Cernak providing a screen.
"We were playing the same way the whole 60 minutes," Cernak said. "In the Detroit game (a 4-2 win on Tuesday) we played really well the first period and kind of slowed down. We knew what we had to do tonight."
Frank Nazar appeared to cut the deficit to 2-1 at 15:04 of the second period, but video review confirmed the call on the ice that the puck was hit with a high stick before it went into the net.
"It definitely feels like some things aren't going in right now," Blackhawks defenseman Alex Vlasic said. "Sometimes teams go through that, but I think we found a bunch of chances where we almost have a couple of good looks and nothing seems to be going in the net for us right now."
McDonagh extended the Lightning lead to 3-0 at 2:38 of the third period when he beat Soderblom high to the glove side with a slap shot off a pass from Jake Guentzel.
Mikheyev made it 4-0 at 5:08 with a tip-in from the blue paint off a cross-ice pass from Cernak.
"If you play at home and you score an early goal it's a huge advantage," Mikheyev said. "You feel confident right away, and it's more comfortable, of course."
Mikheyev spent the past two seasons with the Blackhawks before signing a four-year, $15.4 million contract (average annual value of $3.85 million) with Tampa Bay on July 1.
"How about that, he gets to play against his old team and scores two," Cooper said. "That's pretty cool. Good for him."