It was Johnston's first hat trick of the season and fourth in the NHL.
Jason Robertson had a goal and two assists, Mikko Rantanen had three assists, and Roope Hintz had two assists for Dallas (17-5-4), which has won four in a row and is 5-0-1 in its past six games. Casey DeSmith made 15 saves.
Jake Sanderson scored for Ottawa (12-9-4), which has lost three of its past four games (1-3-0). Linus Ullmark made 20 saves.
Mavrik Bourque gave Dallas a 1-0 lead at 1:58 of the second period when Ilya Lyubushkin’s shot from the right point deflected in off him at the left post.
Lyubushkin had missed the previous six games with an lower-body injury.
Sanderson tied the game 1-1 at 8:36, scoring five-hole from the left circle after Shane Pinto forced a turnover by Jamie Benn along the right boards.
Robertson put Dallas back in front 2-1 at 9:20. After Tim Stutzle lost control of the puck along the boards, no Senators player went to pick up Robertson, who skated slowly into the slot before beating Ullmark glove side.
Robertson has scored a goal in nine of his past 10 games (13 goals during span).
Johnston extended the lead to 3-1 at 15:33, scoring on a one-timer in front off a backhand pass from Rantanen, who was behind the net.
Johnston then made it 4-1 with a power-play goal at 2:52 of the third period, and Benn pushed it to 5-1 at 7:24 by tapping in a backdoor pass from Rantanen.
Johnston completed the hat trick at 15:41, scoring his second power-play goal from the low slot off a short pass from Hintz to make it 6-1.
It was Johnston's 16th goal of the season and his League-leading 12th on the power play.
