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Astra quaified for the Champions League after winning the Romanian title for the first time and ending Steaua Bucharest's three-year domination, but they bowed out in the third qualifying round earlier this week after losing 4-1 on aggregate following a 3-0 defeat in Denmark.
A mild rivalry also exists with Steaua București. In early 2016, at the time when the two clubs fought for the championship title, the non-playing staff of both sides often engaged in disputes via press statements.
But they could not break down a stubborn Astra side, who have only won once in five league games this season but went through on Thursday by converting one of just two shots they had on target.
All that hard work last season was for nothing. So were all those draining qualifying games this summer. West Ham United’s attempt to reach the group stage of the Europa League ended in familiar frustration, because of both the manner of the defeat and the identity of their conquerors.
Astra will be familiar opponents for West Ham as they played them in the third qualifying round of the Europa League last year, exiting 4-3 on aggregate after losing the second leg 2-1 following a 2-2 draw in the first leg at Upton Park.
To put Astra’s achievement into context, they lost 5-1 to CFR Cluj last Sunday and have a manager, Marius Sumudica, who cannot attend his team’s domestic matches after being banned by the Romanian Federation for betting on games. “This is one of the best days in my life, on pretty much the same level as when my children were born,” a jubilant Sumudica said. “Because I knew that they were mine. Obviously I’m kidding.”
Domestically, Astra's major honours include one Liga I, one Cupa României and two Supercupa României. They qualified for the very first time in a European competition in 2013, playing in the UEFA Europa League.
Argentine striker Calleri missed two golden chances, one either side of the break, with only Fletcher - a young forward signed from Manchester United this summer - providing real spark when he came on shortly after the hour mark.
West Ham have won only one of their last six European games, all Europa League qualifiers (D2 L3).
At least Ashley Fletcher, a summer signing from Manchester United, showed no fear after replacing Calleri. The young forward scared Astra with his direct running, appealing for a penalty after a risky tackle from Teixeira; and a superb save from Lung denied him his first goal in claret and blue.
Both teams moved directly into the group stage after finishing fifth and sixth in the Premier League last season, above seventh-placed West Ham.
But West Ham could not avoid a first competitive loss at the London Stadium.
Slaven Bilic's side reached the play-off round this year by defeating Slovenia's NK Domzale 4-2 on aggregate thanks to a 3-0 victory in the first competitive match at their new London Stadium home on Thursday night.
In contrast, the Hammers had 17 unsuccessful attempts at goal - again highlighting Bilic's need for attacking reinforcements.
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West Ham are left to focus solely on their domestic season. Next up is a Premier League trip to Manchester City, who have won both of their opening matches, on Sunday (16:00 BST).
These are the International Federation of Football History & Statistics (IFFHS) club's points as of January 2016:
In the summer of 1992, Astra were promoted for the first time to the Divizia C. The following seasons it finished 6, 12, 3 and 14 in the championship.
Andy Carroll and Aaron Cresswell (both knee) are both missing for the hosts.
After the break West Ham's Jonathan Calleri and Winston Reid missed good chances and Ashley Fletcher went close.
Although Astra Giurgiu have lost five of their last seven away European games (W1 D1), their two unbeaten games were on British soil, winning 1-0 at Inverness and drawing 2-2 with West Ham in 2015.
Burke’s heavy headed touch invited a tackle and West Ham were exposed when the young left-back sold himself, leaving his fellow defenders outnumbered as Astra countered. With both full-backs out of position Daniel Niculae fed Teixeira, the Portuguese midfielder formerly of West Bromwich Albion, who gave Astra control of the tie for the first time.
The ties will take place on Thursday August 18 and Thursday August 25 with the Hammers drawn away in the first leg.
The Hammers have won three of their last four Europa League home qualifiers (D1), although those games were all played at Upton Park.
On 18 September 1921, weekly newspaper Ecoul Sportiv announced the founding of the Clubul Sportiv Astra-Română ("Astra-Romanian Sports Club") by the Astra-Română Society, an oil-company owned by Henri Deterding and based in Prahova, composed of English, American and Dutch officials.
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This is the UEFA club's coefficient as of 26 August 2016:
The France midfielder is almost match-fit but is unlikely to be risked, although Bilic said either he or Manuel Lanzini (knee) may be on the bench with the tie firmly in the balance.
Andre Ayew (thigh) does not need surgery on the thigh injury he sustained in the opening day defeat at Chelsea but is still absent alongside Diafra Sakho (back) and Sofiane Feghouli (hamstring).
The tie is evenly poised at 1-1 ahead of Friday's group stage draw after Mark Noble's penalty was cancelled out by a late equaliser from Denis Alibec in last week's first leg.
Astra Giurgiu have shipped 26 goals in their last 12 away European games, keeping only one clean sheet (1-0 v Inverness).
The club plays its home matches in Giurgiu at the Marin Anastasovici Stadium, having moved here in September 2012, with the former Astra Stadium based in Ploiești now acting as a training ground. It has a current capacity of approximately 8,500 spectators.
After a 1-1 away draw last week, West Ham went behind when Filipe Teixeira precisely finished a swift counter-attack by the Romanian champions.
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"If we want to qualify, we have to beat Astra at home and we should be confident. I expect us to win."
Italian giants Inter Milan, Dutch runners-up Ajax and Spanish side Athletic Bilbao are all potential opponents for the English pair, along with Dundalk, who fell short of becoming the first Irish team to reach the Champions League group stage.
The Hammers' exit from Europe's secondary club competition leaves Manchester United and Southampton as the only English sides in Friday's draw.
Astra Giurgiu have only qualified for the Europa League once before, in 2014/15. They were eliminated in the group stage.