It was Hemsky's second game and first points with Ottawa since he was acquired last Wednesday in a trade with the Edmonton Oilers and slotted on to the Senators' top line.
Craig Anderson stopped 46 shots for the Senators.
Turris's goal was his 21st of season, while it was Hoffman's first of the season. Hoffman and Michalek also picked up an assist.
The Jets have lost three straight, including overtime against the New York Islanders and in regulation versus Los Angeles.
Winnipeg went into the game three points back of Dallas for the final wild-card playoff spot in the Western Conference and one point behind Phoenix, which visits Washington Saturday night.
Ottawa was six points out of a playoff berth in the Eastern Conference before the game.
The Senators led 2-1 after the first period and 5-2 following the second.
Michalek scored his 11th goal of the season at 9:54 of the opening period with a deflection off a Jets' defender just 20 seconds after defenceman Zach Bogosian went to the penalty box for holding.
The goal was reviewed to see if the puck had fully crossed the line behind Pavelec.
With Ottawa winger Chris Neil off for interference, Little got his stick on a rebound and sent a backhand shot over a stretched-out Anderson at 16:59.
But the tie was short-lived as Cowen's goal came 38 seconds later off a shot from the point.
Winnipeg had a two-man advantage for 70 seconds in the period, but couldn't capitalize.
Gryba scored 2:03 into the second period during a play that had Jets defenceman Mark Stuart sliding into Pavelec, sending him rolling at the side of the net.
Winnipeg regrouped and Evander Kane won a faceoff and sent it back to Enstrom, who blasted a shot past Anderson at 4:15 while Ottawa's Cowen was off for slashing.
Turris soon took a pass from Hoffman as he was going behind the net and beat Pavelec at 8:58 to make it 4-2.
Ottawa sent Pavelec to the bench in favour of Montoya when Hoffman made it 5-2 at the 936 mark of the second period.
Winnipeg had outshot the Senators 27-25 after the second period.
Byfuglien scored unassisted with a slapshot 2:13 into the third period for his 14th goal of the season.
Ottawa was 2 for 4 on the power play and the Jets were 2 for 7.
Winnipeg travels to Colorado for a game Monday and then hosts Vancouver on Wednesday. The Senators host Nashville on Monday.
Notes: The Jets are now 11-5-2 since head coach Paul Maurice took over on Jan. 12.