The Hammers looked to be heading for all three points after Manuel Lanzini added a second for West Ham with just four minutes left on the clock.
But the the home side failed to hold on and Evans rose the highest in the box four minutes into injury time to head the ball past Darren Randolph.
It was harsh luck on Slaven Bilic's side who were outstanding throughout the ninety minutes and deserved more from the game after Sofiane Feghouli had cancelled out an early goal from Nacer Chadli.
Despite the late heartbreak, the Hammers can still take a number of positives from the game as they now prepare for a short break before the next Premier League game against Watford on 25 February.
The Hammers may have been missing influential forward Andy Carroll through injury, but his team-mates once again showed their fighting spirit and were unlucky to only come away with a point.
West Brom got off to a dream start when they opened the scoring after just five minutes.
James Morrison fed the ball into Chadli who took the ball past Cheikhou Kouyate and fired the ball past Darren Randolph into the corner of the net.
The Hammers almost found an immediate way back into the game on 12 minutes when Robert Snodgrass saw his powerful left-foot free-kick produce a superb save from Ben Foster diving low to his right.
West Brom could have doubled their lead on 15 minutes when Salomon Rondon lifted the ball up and fired a fierce volley from the edge of the box which beat Randolph, but his effort cannoned back off the bar.
The game then erupted into controversy on 17 minutes after Feghouli raced onto Manuel Lanzini's pass and fired the ball into the corner of the net.
But referee Michael Oliver disallowed the goal after Craig Dawson went down injured inside the box.
The decision infuriated the players and home supporters who felt there was no infringement in the lead up to the goal.
The Hammer had another golden opportunity to draw level on 31 minutes after Ben Foster fumbled a corner from Snodgrass.
When the ball dropped down Antonio failed to find any kind of connection which would have seen the ball cross the line and Matt Phillips was able to clear the danger.
The home side then had strong claims for a penalty turned down after Livermore appeared to bring down Snodgrass inside the box but referee Oliver waved for play to continue, much to the fury of the home crowd once again.
The Hammers finally got back on level terms on 63 minutes and it was ironic that Feghouli was the man to bring the home side level, following his earlier effort which was ruled out.
Manuel Lanzini picked up the ball on the edge of the box and fired an unstoppable shot which Foster tipped onto the bar.
The rebound fell nicely to Feghouli and he made no mistake striking the ball into the back of the net.
Lanzini thought he had won the game for the Hammers on 86 minutes as he raced onto a ball from Lanzini and fired a powerful shot past Foster into the corner of the net.
But Evans broke the hearts of the home faithful when he rose the highest to flick the ball past Randolph and the Hammers had to settle for a point.
West Ham XI: Randolph; Kouyate, Fonte, Reid, Cresswell (Calleri 78); Feghouli (Collins 90), Noble, Obiang, Snodgrass (Fernandes 88); Antonio, Lanzini
Subs not used: Adrian, Byram, Nordtveit, Fletcher
Bookings: Obiang, Reid
West Brom XI: Foster; Nyom, Dawson, McAuley, Brunt; Livermore, Fletcher; Chadli (Evans 52), Morrison (Yacob 78), Phillips (Robson-Kanu 67); Rondon
Subs not used: Myhill; Olsson, M Wilson, McClean
Bookings: Rondon, Brunt
Referee: Michael Oliver
Attendance: 56,983