The teams split six goals in the first period, but Ottawa was shut down after that. Schremp made it 4-3 at 1:39 of the third with a power-play goal. Frans Nielsen sealed the win with a short-handed, empty-netter with less than 10 seconds to go.
Ottawa (17-28-8) is 1-11-4 in its last 16 games. Its only win in that span was against the Islanders on Jan. 13.
Matt Moulson and Michael Grabner also scored for the Islanders. Chris Neil, Mike Fisher, and Alex Kovalev all had first-period goals for Ottawa.
Senators goalie Brian Elliott was pulled after allowing three goals on 13 shots in the first period. He was replaced by Robin Lehner, who had an active second period.
Lehner nearly instigated a brawl at the end of the period by elbowing Islanders goalie Kevin Poulin as they skated past each other, and was given a minor penalty. With 2:40 left in the frame, Lehner appeared to punch John Tavares in the back of the head in front of the crease.
Lehner's end-of-period penalty, coupled with Chris Phillips' interference infraction, gave the Islanders a 5-on-3 power play for the first 1:55 of the third.
Schremp tapped a rebound of Travis Hamonic's shot past Lehner at 1:40. It was Schremp's second of the game and ninth of the season.
New York and Ottawa are ranked 28th and 29th in the NHL in goals, ahead of only New Jersey, but they staged a wild first period. Only New Jersey has scored fewer goals than the Islanders and Senators.
Ottawa scored three times on six shots in the period, and all six goals came with the teams at even strength. The Islanders finished with a 37-23 shots advantage overall.
Moulson made it 1-0 4:10 in by roofing a rebound of Jack Hillen's shot over Elliott, but Neil tied it 13 seconds later.
Poulin lost the puck to Fisher behind the net, and the Ottawa center fed Neil for an easy goal.
Grabner snapped a rebound of Nielsen's shot past Elliott at 9:44 for his 16th goal. Fisher's 14th at 12:20 made it 2-2.
Kovalev gave the Senators their only lead at 17:11 with a shot from the right circle. The edge lasted only 17 seconds as Schremp one-timed a rebound of Jeremy Colliton's shot to make it 3-3.
It stayed that way until Schremp put the Islanders in front for good in the third.
Lehner was solid in relief, allowing only one goal and making 23 saves.
Notes: Islanders RW Blake Comeau sat out because of a concussion sustained in Wednesday's loss at Pittsburgh. There is no timetable for his return. ... Comeau joins G Rick DiPietro on the list of Islanders injured in the loss. DiPietro will miss 4-to-6 weeks with facial fractures and swelling in his knee after being dropped with one punch by goalie counterpart Brent Johnson in the final seconds. New York recalled G Mikko Koskinen from AHL Bridgeport. ... The Islanders also signed G Joel Martin from Odessa of the Central Hockey League and assigned him to Bridgeport. ... Ottawa D Matt Carkner missed a second game because of an undisclosed lower body injury. He is expected to return this week.