The Reds were desperate for a return to winning ways after they drew 1-1 with Leicester City last week, while City defeated Arsenal on Sunday to close the gap to two points.
Sadio Mane gave the visitors the lead in the 22nd minute with a composed finish from six-yards out after being picked out by James Milner.
Six minutes later, the home side were level as a clever free-kick from Felipe Anderson played in Michail Antonio, who found the back of the net with a neat finish from close range.
Jurgen Klopp's charges were unable to find a way past the the Hammers defence in the second half as they were forced to settle for a share of the spoils.
Lazio moved up to seventh spot in the Serie A standings with a 1-0 victory over Frosinone at the Stadio Benito Stirpe.
Felipe Caicedo got the game's only in the 36th minute to take his tally for two goals for the campaign.
Hans Hateboer's 50th minute strike was enough to hand Atalanta a 1-0 win away to Cagliari and secure sixth spot in the standings.
Leganes moved out of the relegation zone after defeating fellow strugglers Rayo Vallecano on Monday night.
Martin Braithwaite hand the visitors the lead after 36 minutes, before they were reduced to ten men when Allan Nyom received his marching orders on 58 minutes.
Alvaro Garcia restored parity for Vallecano in the 83rd minute, but Leganes had the final say with Youssef En-Nesyri netting the winning goal two minutes later.