Sheary had a goal and an assist, and Ilya Samsonov made 24 saves for his first shutout of the season for the Capitals.
Scott Wedgewood made 27 saves for New Jersey (12-16-4), which was swept in the back-to-back set. Washington won 4-3 here Thursday.
"Well, we lacked energy for sure," Devils coach Lindy Ruff said after their fifth game in seven days. "I don't know whether the schedule caught up to us, but it was teamwide, and when you don't have energy you're not skating as well, you're not executing as well. We made some poor decisions early before we could even get into the game, and those decisions hurt us dearly."
Several of New Jersey's best chances came in the opening minutes, but Samsonov made saves that set the tone.
"Anytime you get some early good saves, you feel more comfortable and stay in the game," Samsonov said. "I like it. ... I think every goalie likes it."
Ovechkin gave the Capitals a 1-0 lead at 5:58 of the first period. He entered the offensive zone and dropped the puck to Evgeny Kuznetsov above the left face-off circle, took a return pass across the slot and scored on a wrist shot from the bottom of the right circle.
Nicklas Backstrom scored off a pass across the crease from Tom Wilson to make it 2-0 at 11:50.
"I think we played with speed," Wilson said. "We forechecked them well. We've got experience on our side and we wanted to take it to them early, take away their time and space. I think for the most part we did it."