Hull head to London two points ahead of Allardyce's men.
Bruce said: "If you're going to pick a manager to get you out of trouble, you couldn't do any better than Sam. I'd have every penny I've got on West Ham to stay up.
"As soon as they got Andy Carroll back from injury, it was only a matter of time before they got going.
"They were going to some places without any strikers at all because of the situation they found themselves in. If you're in and around it. The one thing you need is your big players fit, I don't care who you are.
"If four or five of your best players aren't playing, it's going to be a struggle for you.
"Most squads can't deal with missing four or five players."