After the break it was a different story as Villa could have nicked the game but Christian Benteke hit the bar late in the match.
Sports Mole analyses the game at Upton Park to see if the result was a fair one.
On target 4
On target 2
Was the result fair?
Villa had the better clear-cut chances to win the game late on but the Hammers dominated possession and, on the merit of the match, they should not have left without anything for all their hard work with the ball, so a point is a fair reflection of the game.
West Ham's performance
Sam Allardyce's side dominated the first half and created a few opportunities which Matt Jarvis and Stewart Downing could not take. For all their possession, there were never any clear-cut chances. Playing without a striker really hurt them as it allowed the Villa defence to play a high line and sniff out any danger that came their way. After the break they ran out of ideas and were nearly undone on the break by the visitors but they held out for the point. Given their recent form at home, Allardyce will be pleased.
Aston Villa's performance
Lambert will be pleased that his side executed their game plan perfectly. They defended in numbers when the Hammers had the ball in threatening areas and hit them on a swift counter-attack on more than one occasion as Andreas Weimann nearly benefited in the first half and Benteke in the second. Lambert's men could have left with the three points if Benteke's header had not clattered off the bar and went in the net instead, but given their gameplan and West Ham's dominance of the ball, the Scot should be happy.
Sports Mole's man of the match
Ron Vlaar: The defender was a solid presence at the back for Villa throughout the game. He won all the battles in the air and made several excellent tackles for his side inside their own box to deny the Hammers chances at goal. He led from the front and was crucial in earning his side a point.
Nathan Baker's botched clearance in the first half almost gave Jarvis a chance to slot the ball home but he was bailed out by a good save from Brad Guzan. The defender looked quite relieved after he missed his kick to present the former Wolverhampton Wanderers man with the chance.
Howard Webb's performance was fine. He let the game flow as much as he could and was not quick to give out bookings. The yellow cards he gave were just as Matt Lowton and Leandro Bacuna were guilty of poor challenges.
West Ham: The Hammers travel to face Norwich City at Carrow Road next Saturday.
Aston Villa: Paul Lambert's side face Cardiff City in their next Premier League outing at Villa Park on November 9.