When you have not scored in 11 hours and 41 minutes of Premier League football, any goal is welcome and it was fitting that Sunderland's first arrived in freakish style.
Moyes' side conceded in the first minute of the second half in last week's 3-0 loss to Manchester United and they seemed not to have learned their lesson, as Collins headed West Ham back in front soon after the break.
A worrying injury for Billy Jones led to 10 minutes of injury time being added on, and Sunderland could not find a victor despite Sam Byram being sent off in the 95th minute.
Sunderland are now nine points from safety with only six games of the season remaining.
The game was just seconds old when midfield enforcer Lee Cattermole was booked for a trip on Ayew on the edge of the box, and keeper Jordan Pickford had to dive to his left to parry Manuel Lanzini's second-minute free-kick.
Meanwhile, Sunderland boss, David Moyes, said: "I thought we played well today.I thought from the start we tried to get after them right away".
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Jones was taken off on a stretcher after he landed heavily following a tussle with Arthur Masuaku, with Moyes throwing on an extra attacker in the form of Borini after a long delay, and that boldness paid off as the Italian levelled in the 90th minute. They had the ball, but they were playing very risky, leaving a lot of space behind.
Byram was then dismissed for West Ham well into stoppage time after being shown a second yellow card, but it was too late to benefit Sunderland.
Wahbi Khazri, starting for the first time since October 29, scored direct from a corner for Sunderland in between.
Ahead of the match, West Ham vice-chairman Karren Brady has given her opinion on Sunderland's situation.
"We want Moyes out", chorused home fans after André Ayew gave Slaven Bilic's visitors a fifth-minute lead and the crowd booed the Scot every time he ventured out of his dug-out, including when he went to collect a couple of loose balls.
A win at home against West Ham would help their cause immensely.