After a quiet start to the match, the Hammers slowly started pressing the visitors, with their front three of Dimitri Payet, Enner Valencia and Mauro Zarate linking well.
At the other end of the pitch, Italy international Angelo Ogbonna made his competitive debut as was expected, playing as the left-sided centre half alongside James Collins.
They were kept busy too, with ex-West Bromich Albion midfielder Phillepe Texeiria going agonisingly close to opening the scoring on 20 minutes, but finding the side netting instead.
Payet influence already making a difference
Star signing Payet's influence grew and grew, though, and after some probing it was his exquisite cross to the far post for Valencia which did break the deadlock on 23 minutes.
The Frenchman has got Hammers fans excited ahead of the new season and it was easy to see why.
His initial corner was headed back to him, and just as he did in the pre-season friendly at Norwich on Tuesday the second cross was bang on the money, picking out his Ecuadorian teammate who rose highest to head home.
Astra were supposed to be the toughest test yet in the Europa League for Slaven Bilic's side given the fact they made last season's group stages after beating French giants Lyon before taking the scalp of Dinamo Zagreb.
But the Hammers clearly raised their game to mitigate the tougher opposition after matches against Andorran minnows Lusitanos and Maltese side Birkirkara in previous rounds.
Double injury blow for Hammers
The half ended on a sour note, though, with Joey O'Brien being withdrawn on 37 minutes after feeling a hamstring. At the same time goalscorer Valencia also went off with what looked like a serious injury after getting his leg caught when making a challenge.
Youngster Reece Burke and outcast Modibo Maiga replaced them.
It didn't seem to impact on the hosts' dominance, though, as the Hammers ended the half with nearly 67% possession and 10 corners and should have gone 2-0 up when Zarate's fine curling effort was brilliantly turned around the post by the Astra goalkeeper.
There was no doubting the star of the show so far as Payet showed his prowess throughout, constantly looking to get on the ball and make things happen.
And there are encouraging signs too for Hammers fans who were yearning a more attacking style of play in line with the club's roots with the ball being played around nicely by the Irons.
West Ham 1 Astra Giurgiu 0.