West Ham led twice through goals from Pablo Fornals and Michail Antonio, and although it may feel like a missed opportunity for Moyes' men, the visitors were good value for the draw after being the better side for large periods of the second-half.
This fixture has a bit of habit of producing some world-class goals, Dimitri Payet's stunning free-kick at Upton Park being one, and the pattern continued with the opener today - Pablo Fornals finishing a quality move after great link-up with Michail Antonio.
Viera's men improved after the interval and Gallagher equalised from a tight angle on 58 minutes.
Antonio made it 2-1 with his 50th Premier League goal 10 minutes later, but the Hammers' lead didn't last long as the Chelsea loanee got a second to draw Palace level.
All in all a very entertaining fixture with a draw the fair result.
Story of the match
There were few moments of significance inside the first 15 minutes as both sides looked to figure out one another, a tense London derby with little to separate the two sides.
The Hammers' first big chance fell to the feet of an unlikely candidate, no-nonsense centre-half Craig Dawson swivelling and shooting inside the box, but his effort was scrambled clear.
Their next opportunity involved a more regular goalscorer, Michail Antonio causing problems in the box as he sought his 50th goal in the Premier League. He attempted to meet Vladimir Coufal's delivery, and Joel Ward was forced to clear off the goal line after Vicente Guaita ended up in no man's land.
Palace found themselves weathering a storm with 25 minutes on the clock, and their resistance was almost broken down when Aaron Cresswell found space in behind, his final ball almost gifting a teammate a great chance - the story of West Ham's first half hour.
Said Benrahma released Antonio, and after a combination of delicate passes inside the box between Antonio and Fornals, the ball was returned to the Spaniard who rolled it into the bottom corner. A fantastic move from the hosts who displayed great chemistry and composure in attack to get a deserved goal.
There was hardly a chance to report for the South Londoners in the first-half, their struggles to create continuing in the early days of Patrick Viera's tenure. They went in at the break 1-0 down, having failed to trouble Lukasz Fabianski, and were probably fortunate to have only conceded one.
West Ham United (@WestHam) August 28, 2021
No changes were made by either team at the interval, and despite the away side enjoying some early second-half possession, Moyes' men continued to look more dangerous going forwards. Benrahma's strike on 50 minutes was comfortably saved as he aimed to extend his side's lead.
Wilfred Zaha struggled to influence the game in the first-half, but he had a good opportunity to attack the hosts after latching on to a ball over the top. He drove at Coufal with speed, however the shot that followed went well over.
Although against the run of play, Crystal Palace equalised just before the hour-mark through Conor Gallagher, the Chelsea loanee latching onto a loose ball in the box and scoring past Fabianski from a tight angle after showing good perseverance.
The goal to make it 1-1 was the Eagles' first of the season, and seemed to give them some much-needed confidence as they grew into the game. Viera's team enjoyed a good spell after drawing level, putting pressure on the home team with a succession of corners and beginning to provide striker Christian Benteke with some service.
However. West Ham then regained the lead on 68 minutes as Antonio bullied Joachim Andersen to win a high ball over the top, and he took one touch before thundering a finish past Guaita with his left foot.
The frenzy of action continued with Palace making 2-2 just minutes after conceding, Gallagher completing his brace by showing superb skill inside the box before firing it into the back of the net.
Heading in to the final 10 minutes each team felt like they had an opportunity to find a late winner, both managers looking to their bench for some inspiration with Andriy Yarmolenko and Jeffrey Schlupp introduced to the action.
Marc Guehi had a great chance to win the game at the death, rising highest to meet Gallagher's whipped free-kick, and he should have done better with his header from close-range.
Despite a late counter-attack opportunity for the hosts, neither side found a winner, and the spoils were shared at the London Stadium.