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It was Guzan who kept the scores level seven minutes later when Matt Jarvis latched onto a through-ball from Nolan, the American pulling off an impressive stop from close range to keep the Hammers out.
West Ham came close again just after the half-hour mark, with Downing's cross from wide on the right headed inches wide by Jack Collison.
The Hammers almost took the lead in the 58th minute when a free kick from Jarvis fell to Collison, whose volley from the edge of the box sailed narrowly over the crossbar.
At the other end of the pitch, Villa were denied by the woodwork as Benteke's header from a Matt Lowton cross came back off the underside of the bar.
West Ham pressed for a winner in the latter stages with efforts from Nolan and Joe Cole, but the deadlock remained intact.