Carlton Cole produced a delightful overhead kick to put West Ham ahead after eight minutes before Darius Vassell stabbed in a controversial equaliser eight minutes later.
The Hammers always looked more likely to pilfer the points, however, and Hart confirmed his rich promise with excellent saves to deny Mark Noble and then Cole in the closing stages.
City boss Eriksson said: "He played very well yet again today. He has a great future and is a fantastic goalkeeper for his age.
"He's rather big, he's good on crosses and he's very brave.
"The only thing that's missing is experience. You cannot buy experience - you have to stand there between the posts and let it happen over the years."
Back in August and September, Kasper Schmeichel was Eriksson's number one and Hart also appeared to have Andreas Isaksson standing in his way once the experienced Sweden international returned from injury.
But, after taking his time to have a good look at his options the Swede decided to pin his hopes on Hart, declaring him number one until further notice.
Hart has repaid Eriksson with interest and while the England Under-21 international Hart has played down his own chances of being included in Fabio Capello's senior squad, his performances are making a compelling case for his inclusion.
"I said weeks ago that he has the chance to be an England goalkeeper in the future," added Eriksson.
"I don't know whether it's time now - Capello has to decide that - and I'll be happy with whatever happens.
"I don't think Joe Hart expects to be in the full side. He's the youngest goalkeeper we have."
West Ham deserve credit for producing a spirited response after limping out of the FA Cup at Eastlands four days earlier.
That they did so without Dean Ashton and Matthew Etherington - both ruled out due to back and knee injuries respectively - hinted at the depth and quality of their squad as the Londoners continue their own assault on Europe.
The Hammers were already shorn of the services of a host of key players and manager Alan Curbishley said: "Hart has been excellent in the two games and is probably the reason why we've not won both of them.
"I'm a little bit disappointed but it's great credit to the players that they deserved to be the first team to win here.
"We've had to chop and change all season and there's been great disruption to the squad, but they've done fantastically well.
"And if we can get one or two back - and freshen it up and carry on being as committed as we are - we'd like to finish in the top eight.
"First we need to catch the two teams above us - Blackburn and Portsmouth - but the signs are very encouraging."