The Hammers went into the match on a run of nine games against Newcastle without a win, but began confidently and took the lead on eight minutes.
Home debutant Di Michele cut in from the right wing and skipped through two challenges before his shot looped into the back of the net off Taylor.
Mark Noble almost made it two with a free-kick which flashed just over the bar, but after that Newcastle settled and came more into the match.
Zola delighted with first home win
With Julien Faubert playing out of position at right-back, Newcastle's left winger Damien Duff looked particularly threatening, and he could well have had a penalty when his cross seemed to hit midfielder Scott Parker's arm.
Geremi and Charles Nzogbia also looked promising for Newcastle, but Green's goal rarely came under serious threat, and when the next breakthrough came, it was another for Di Michele.
Noble's finely judged pass put the Italian through on goal and although Given blocked his initial effort with his head, he showed wonderful composure to juggle the ball and drill a low shot into the bottom corner.
Can't fault Magpies for effort - Hughton
Newcastle had to wait until the second half for their first effort on target, but Xisco got in Owen's way and he could only produce a weak header.
Instantly they were made to pay for it as West Ham extended their lead, di Michele unselfishly setting up Etherington to roll the ball into the net.
Owen gave his side hope when he caught Lucas Neill off-balance and found the net with a low curling shot in the 67th minute, and this seemed to revive the visitors.
Green did well to deny Nzogbia as West Ham's energy level and concentration seemed to dip, but they held on and in the closing stages substitute Luis Boa Morte wasted two great chances to make the win even more convincing.
West Ham manager Gianfranco Zola:
"In one week I'd like to say we did something to these guys but to be fair to them it's down to them and what Alan Curbishley did so far. The attitude has been incredible.
"We knew already that in the last 20 minutes our condition had gone a bit down, but even in those moments, we kept the shape and tried to maintain good position - I'm very proud of them.
"My duty is to make things work on the pitch, me and all my staff will be working on that, then we need support from (technical director) Gianluca Nani and the board, who will need to do their part - I trust them, they trust me."
Acting Newcastle coach Chris Hughton:
"I thought we came out very well in the second half and once Michael Owen got the goal I genuinely thought we had a chance of getting back in.
If we were going to get something it was from wide, Geremi and Damien Duff. You can't afford to concede so early on, we got back in and played some good stuff but they were soft goals.
"I was very pleased that we had a real go in the second half, it was a spirited performance, we could have got something out of the game.
"The situation's no different to how it was a week or so ago. It'll be best for all when a manager comes in but that's not the situation at the moment but I can't fault the application of the players."
West Ham: Green, Behrami, Upson, Neill, Ilunga, Faubert, Noble, Parker (Mullins 72), Etherington (Boa Morte 73), Di Michele, Cole (Sears 87). Subs Not Used: Lastuvka, Lopez, Davenport, Reid.
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