David Moyes's side earned a 2-0 away win over Dinamo Zagreb, while their visitors suffered a 1-0 defeat at the hands of Genk in their opening game of the group stage.
Match preview
After an impressive sixth-placed finish in the Premier League last season, West Ham United earned automatic progression to this year's Europa League group stage, entering European competition for the first time since they lost to Astra Giurgiu in qualifying in 2016.
They began with a tough trip to take on Croatian champions Dinamo Zagreb, and an early Michail Antonio goal put them ahead, before Declan Rice doubled the lead in the second half, sealing an impressive opening win.
David Moyes's side have also picked up where they left off on the domestic front so far, sitting in seventh spot in the English top flight with 11 points from six games.
After going unbeaten in the first four league matches, the Irons were handed a narrow defeat by Manchester United, but have since bounced back in style, defeating the Red Devils three days later in the EFL Cup, before returning to winning ways in the Premier League when they took on Leeds United last time out.
Raphinha put their opponents ahead in the first half, but a Junior Firpo own goal drew the Moyes's men level, before Michail Antonio hit a 90th-minute winner to snatch all three points for his side.
They will now look to build on that with what would be another crucial victory in their bid to reach the Europa League knockout stage, but face a tough test against a Rapid Vienna side who will look to put their first points on the board.
After earning a second-placed finish in the Austrian Bundesliga last term, Rapid Vienna earned a spot in the qualification rounds for the Champions League, and they managed to defeat Sparta Prague 2-1 in the first leg of their second-round tie, only to lose 2-0 away from home and drop into Europa League qualification.
Dietmar Kuhbauer's side defeated Cypriot outfit Anorthosis 4-2 over two legs, before cruising past Zorya in the final qualification round to reach the group stage.
Their start to life in the group did not go to plan, as their home clash with Genk looked set to end goalless, only for Paul Onuachu to snatch all three points for the visitors with a 92nd-minute winner.
That added to a disappointing run of form for Die Grun-Weissen, who have now won just one of their last six games in all competitions, and lost 3-0 to Sturm Graz in the Austrian Bundesliga last time out, seeing them drop to second-bottom with eight points from nine games.
Kuhbauer's side will now be desperate to arrest that slump in form and boost their qualification chances, but face a particularly tough challenge as they travel to East London.
West Ham United Europa League form:
West Ham United form (all competitions):
Rapid Vienna Europa League form:
Rapid Vienna form (all competitions):
Team News
While David Moyes sent a particularly strong starting XI to Dinamo Zagreb, he could opt to give starts to several squad players on Thursday, given their increasingly hectic schedule.
That should see Alphonse Areola feature between the sticks, while the likes of Craig Dawson, Arthur Masuaku and Manuel Lanzini could be lined up to start.
Attacking midfielder Nikola Vlasic made his first start in the group opener, and he should again feature throughout on Thursday, while Alex Kral recently arrived on loan from Spartak Moscow, and could give a rest to either Declan Rice or Tomas Soucek in the engine room.
Rapid Vienna will be without several players for Thursday's clash, with Christopher Dibon, Richard Strebinger, Oliver Strunz and Lion Schuster all sidelined through injuries.
Given they came close to securing a result against Genk, they should field a relatively similar side, with Taxiarchis Fountas and Ercan Kara set to lead the line.
West Ham United possible starting lineup:
Areola; Johnson, Dawson, Ogbonna, Masuaku; Rice, Kral; Vlasic, Lanzini, Yarmolenko; Antonio
Rapid Vienna possible starting lineup:
Gartler; Stojkovic, Greiml, Hofmann, Ullmann; Arase, Aiwu, Grahovac, Grull; Kara, Fountas
We say: West Ham United 3-0 Rapid Vienna
Even if Moyes deploys a rotated squad, West Ham still boast more than enough quality to get past their visitors on Thursday.
The trip to Croatia showed their desire to succeed in this tournament, and we expect the Irons to post another dominant victory to take control in the group.