Jason Roberts' close range finish gave the visitors a 12th minute lead that they held on to for a long period of the game despite a second half onslaught on Paul Robinson's goal by the Hammers.
Manuel Da Costa's header was cleared off the line in the first half but it was after the interval when Avram Grant's side created a host of chances, including efforts from Demba Ba and Carlton Cole, but they failed to convert any of them until German midfielder Hitzlsperger fired in from outside the box with 12 minutes remaining.
Substitute Robbie Keane then failed to connect to a low cross before Blackburn skipper Chris Samba blocked from Carlton Cole in injury time to keep the sides level.
That point means West Ham are now three behind Wigan in 17th after the Latics recorded an impressive 1-1 at Villa Park.
Charles N'Zogbia had given Wigan the lead with his eighth goal of the season on the ten minute mark before Ashley Young's effort beat Ali Al Habsi to level proceedings only seven minutes later.
The game was a fiery affair and Emile Heskey was substituted at half-time against his former club after arguing with the official during the first 45 minutes and reports of a fracas in the tunnel as the teams made their way off for the break.
Birmingham's top flight future is also still in doubt as they lost 2-1 at St.James' Park to a Newcastle side who have broken into the top half of the table.
Shola Ameobi increased Birmingham's relegation fears as he fired Newcastle ahead from the penalty spot after Blues defender Liam Ridgewell was sent off for handball.
Defender Steven Taylor added a second two minutes before the break with a header, but former Newcastle midfielder Lee Bowyer reduced the deficit before half-time when his shot was deflected into the net by Fabricio Coloccini.
Sunderland took a huge stride towards securing their Premier League status with a vital 2-1 win against Bolton at the Reebok Stadium.
Veteran midfielder Bolo Zenden made the breakthrough for the visitors in first half stoppage time when he rounded Jussi Jaaskelainen to tap home after beating the offside trap.
Owen Coyle's side had been in charge until that point and were unlucky not to be ahead after Daniel Sturridge hit the bar.
Ivan Klasnic's goal five minutes from time had looked like earning a deserved point for Bolton until another goal in stoppage time for Steve Bruce's depleted Sunderland side came as on-loan Inter Milan midfielder Sulley Muntari latched on to a through ball from Stephane Sessegnon. His shot on goal was turned into his own net by Zat Knight.
Manchester City failed to put more space between themselves and Tottenham in the race for fourth place after Everton came from behind to beat Roberto Mancini's side 2-1 at Goodison Park.
Yaya Toure put City on course for a potentially decisive win when he struck the opening goal after 28 minutes in a first half dominated by the FA Cup finalists, David Silva particularly shining.
But a second half rally from the Toffees saw them take the three points, former City defender Sylvain Distin drawing Everton level with a powerful header which was too strong for Joe Hart to keep out.
The winner also came from a header as the diminutive Leon Osman beat Vincent Kompany to Phil Neville's pinpoint cross with 18 minutes remaining.