The Hammers went a goal up after just four minutes when Jarrod Bowen's cross was misread by Jamaal Lascelles, which left Michail Antonio free at the back-post to notch the away side in front.
Newcastle pulled level shortly after when Emil Krafth's inch-perfect cross was met gracefully by the Magpies' top scorer Miguel Almiron to tie the game.
The teams were level going into half-time, but Tomas Soucek put West Ham 2-1 up directly from Declan Rice's header which rattled the crossbar.
Newcastle equalised instantly through Jonjo Shelvey, who met Dwight Gayle's through ball and finished cleanly into the bottom-right corner.
The Magpies boss said: "I was happy with the result in the end after going behind twice, not many teams have done that since the lockdown.
"We're disappointed with the start but the response from the team was good," said Bruce.
Bounce back ability
On rescuing a losing position twice, the Newcastle head coach said: "They've shown their resilience, I think that's ten goals in four games which is pleasing.
"Unfortunately we've gifted them the first one and they scored from a set-piece which is disappointing."
Saint-Maximin set for a rest
Steve Bruce almost confirmed that Allan Saint-Maximin will sit out against midweek opponents Manchester City, when he said: "Unfortunately I don't think I could ask Allan to go again on Wednesday, that's for sure."
It was revealed that both Sean Longstaff and Isaac Hayden's seasons could both be coming to a premature end, as Bruce said: "Our two, arguably, fittest players in Sean Longstaff and Isaac Hayden have both got hamstring injuries.
"They're not serious but it's two or three weeks which probably rules them out.
"Five games in 15 days in the Premier League is a tough ask.
"We'll see how they all are in the next 24-48 hours."
Bruce frustrated about takeover talk
The Newcastle head coach showed his frustrations on the regular questions on the Magpies' pending takeover: "I am asked this every press-conference.
"I am bored and fed up of answering it.
"Can we move on?"
Matty Longstaff's future not yet finalised
Steve Bruce confirmed that Matty Longstaff's contract negotiations are still ongoing: "They remain ongoing, I will keep plugging away, he will be involved on Wednesday night.
I hope we get it over the line."
Steve Bruce praised Jonjo Shelvey in the final question of his post-match press conference: "If anybody has bought into what we require it's Jonjo.
"He's always been blessed with wonderful football ability but we've worked tirelessly on his physical aspects.
"That's down to him, the stuff he does has all been good.
"He's tried like anything to make it happen."