The Armenian also suffered an ankle injury but could be back as soon as St Stephen's Day
Chelsea continued to boast their title credentials as they took their winning streak to nine games on Sunday afternoon.
Meanwhile, Manchester United edged out Tottenham at Old Trafford thanks to a goal from in-form Henrikh Mkhitaryan, but there was concern when he was subbed off after suffering an ankle injury.
West Ham had the chance to pick up a vital three points and a first win in the league since October, but conceded in the second half and shared the points with Liverpool at Anfield. Both sides benefited from defensive errors and in truth a point does very little for either team.
In the day's only other game, Southampton put their European disappointment in midweek behind them as they picked up a victory at home to Middlesbrough.
We take a look at some of the day's talking points.
It was an afternoon of mixed fortunes for Manchester United midfielder Henrikh Mkhitaryan as the Armenian notched his first Premier League goal for the club but was later stretchered off after an ankle injury.
Mkhitaryan scored his first goal in a United shirt during the week with an excellent solo effort against Ukranian side Zorya. He continued this good vein of form to inspire United to a narrow victory over Mauricio Pochettino's side.
The finish was superb; alive to the danger as the ball broke in midfield he streaked clear behind the Tottenham defence to receive the pass and his first touch pushed the ball into space for him to run into. The shot was rifled past Hugo Lloris in the Spurs goal and United were able to hold on for the win.
There was concern for the midfielder after he was stretchered off with an ankle injury, but United boss Jose Mourinho confirmed that he could be back in the squad as soon as St Stephen's Day.
His change in form will come as a welcome boost for Manchester United who have struggled this season for creativity in midfield and with players still adjusting to playing alongside one another, his ability to link the play will become even more crucial as the season wears on.
United will just have to hope the injury is as minor as it seems.
Jose Mourinho enjoys a first league win since their trip to Swansea at the start of November. Image: Martin Rickett PA Wire/PA Images
The immediate answer: no. Since their 3-0 defeat to to Arsenal in September, Antonio Conte's men have discovered the right blend of defensive solidity and attacking prowess that has seen them win nine Premier League games in a row.
Of those nine wins, they have conceded just four goals and have benefitted from senior players like Diego Costa and Gary Cahill stepping up their performances. Their dismantling of title rivals Manchester City was a statement of how far they've come since that defeat at the Emirates Stadium and they head into Christmas with an even more favourable fixture list.
Upcoming games against strugglers Sunderland and Crystal Palace will make for pleasant reading in this sort of form and affords Conte the chance to rest some key players ahead of a packed festive schedule.
Diego Costa has been in superb form as of late and is the league's top scorer with 12 goals. Image: Tim Ireland AP/Press Association Images
During his commentary today on Off The Ball, Pat Nevin noted that neither side's goalkeepers would be picking up the man of the match gongs and he was dead right.
Ireland number one Darren Randolph gifted the ball to Divock Origi to score the the equalizing goal and reduce the result to just a draw. However, taking into account the run of form they have been experiencing a point away to title chasing Liverpool is a good result in anyone's books.
Question persist over Jurgen Klopp's choice of goalkeeper and the doubts that linger over Liverpool's defensive fragility, an issue that threatens to derail their Premier League challenge.
Should they address the issues over the Christmas, Liverpool will be an excellent proposition to, at the very least, qualify for the Champions League.
But if they continue to leak goals as they have done recently - 10 goals in their last eight games - they may find it difficult to challenge Chelsea come March and April.
Liverpool face Everton and Manchester City in their next four games, two sides who will certainly test their defensive integrity.
Darren Randolph's blunder helped Liverpool salvage a draw from today's game at Anfield. Image: Peter Byrne PA Wire/PA Images