The Hammers struggled to create any chances of note in a poor game at Upton Park and they remain outside of the league's relegation zone by just a point.
Co-chairman David Sullivan had said earlier in the day that manager Sam Allardyce will be at the club until the end of the season but a lacklustre display in front of a largely disgruntled crowd will have done the Hammers boss few favours.
Sunderland defender Phil Bardsley came closest to finding a winner with a long-range pile-driver that came back off the woodwork towards the end of the first half.
Gus Poyet's side need to start picking up wins but, with no league goal away from home since August 31, Sunderland know where their improvement must come from.
The game started at a high tempo as both sides looked to strike early and settle any nerves that would have been prominent at kick-off.
Mo Diame nutmegged John O'Shea and held off Lee Cattermole before cutting a cross back to Modibo Maiga, who blazed over with Wes Brown sliding in.
The same duo linked up again moments later with a deeper cross from Diame headed towards the back post by Maiga, with the in-rushing Matt Jarvis unable to get a telling touch.
The best early chance fell to the visitors as Emanuele Giaccherini slipped a ball into the path of Jozy Altidore but the United States international's shot was tipped behind by Jussi Jaaskelainen.
The corner was only cleared as far as Ki Sung-yueng, whose rasping drive was deflected behind with the Swansea loanee blazing over from a similar position seconds later.
With the game still wide open, Jarvis' cross to the near-post was just missed by James Collins with the ball deflecting behind for a corner.
The Hammers had the ball in the net from the resulting set-piece as Guy Demel bundled it home but referee Andre Marriner had already blown for a free-kick for an infringement.
The early pace of the game was lost as the first half progressed, with Marriner coming under increasing scrutiny from the home fans for giving a number of decisions in favour of the Black Cats.
Their upset turned to anger just before the half-hour mark as Collins was instructed to hurry up with a free-kick inside his own half despite the fact Altidore was clearly not 10 yards back.
The Wales international eventually took the free-kick and it hit Altidore, with Fabio Borini breaking at an unprotected West Ham defence before shooting straight at Jaaskelainen.
Full-back Bardsley came closest to opening the scoring before the interval as his arrowed drive cracked against Jaaskelainen's crossbar with the experienced Finn well beaten.
Ravel Morrison then burst to life with two jinking and twisting runs that left more than one Sunderland defender on the ground but neither resulted in chances for the hosts.
Giaccherini saw a shot deflected behind as the half drew to a close and Demel blocked well from Borini as Poyet's side ended the half in the ascendancy.
Skipper Cattermole had the last meaningful touch of the half as he flashed in an effort that once again required Jaaskelainen to make a save.
The movement of Sunderland's attacking trio of Giaccherini, Borini and Altidore continued to cause West Ham problems at the start of the second-half as the Black Cats started on the front foot once more.
West Ham were still enjoying small spells of possession with the craft of Morrison continuing to look their most likely way through to opening the scoring.
The former Manchester United youngster hit a low shot that was well saved by Vito Mannone before Diame thrashed an effort into the side netting after making space for himself inside the box.
The game reverted back to a pattern similar to the opening exchanges with both sides looking to break the deadlock, although neither Sebastian Larsson nor Giaccherini could test Jaaskelainen with their respective efforts.
Altidore did work Jaaskelainen after a smart turn in the box but the 38-year-old saved comfortably as the game remained goalless with 30 minutes remaining.
Poyet turned to substitutes Adam Johnson and Steven Fletcher to win him the game while Allardyce introduced Carlton Cole from the bench for the final 15 minutes as he looked to give his side more attacking clout.
But it was Sunderland who came close once again as Ki turned inside the box and saw his effort pushed away by Jaaskelainen.
Morrison flashed a shot wide with just under five minutes remaining, with West Ham seemingly shifting their game plan and aiming long balls towards Cole.
Former Sunderland defender George McCartney almost scored a lucky winner deep in stoppage time when his cross had to be tipped over by Mannone as the game ended goalless.