David Moyes’ men had already hit the woodwork twice in the opening exchanges, Declan Rice followed up his goal at Dinamo Zagreb a fortnight ago with another to put his side ahead on the half-hour mark.
And although the game gradually lost its momentum as this entertaining East End evening wore on, Saïd Benrahma struck with virtually the last kick of the tie to cement the Hammers place at the top of the tree.
A spectacular lightshow had marked the return of European football to Stratford for the first time since the early days of West Ham United’s arrival at London Stadium in Summer 2016 and, as both teams strode into an electrifying atmosphere, it was the Hammers, who sparked more rapidly into life than Rapid.
Indeed, with seven minutes on the clock, Aaron Cresswell whipped a deep free-kick into the Austrian area, where Rice rose highest to head the ball on Paul Gartler’s left-hand post but with the visiting ‘keeper well beaten, Issa Diop could only bundle the rebound wide.
Despite being roared on by a raucous bank of green and white travelling fans, Rapid were restricted to early long-range efforts but neither the wayward Ercan Kara nor Taxiarchis Fountas could seriously threaten Alphonse Areola in the hosts’ goal.
The Hammers had made seven changes from the side that had won so well at Leeds United on Saturday as Ben Johnson came in at right-back in place of injured full-back duo Vladimír Coufal and Ryan Fredericks, while Areola, Diop, Craig Dawson, skipper Mark Noble, Andriy Yarmolenko and Nikola Vlašić each received call-ups, too.
But in the stoppage-time allowed for all those switches, West Ham finally got the second goal that their dominance deserved, when Bowen picked out Benrahma in the Vienna area and he curled a low 10-yarder around Stojković into the net to cement the Hammers place at the top of the table ahead of next month’s visit from Belgian outfit KRC Genk who lost to Dinamo Zagreb in tonight’s other Group H fixture.
West Ham Unuted: Areola, Johnson, Cresswell, Dawson, Diop, Noble (Souček 62), Rice, Vlašić (Lanzini 62), Yarmolenko (Fornals 75), Benrahma, Antonio. (Bowen 62).
Unused subs: Fabiański, Randolph, Zouma, Ogbonna, Masuaku, Král, Alese, Baptiste.
Rapid Vienna: Gartler, Ullmann (Auer 73), Aiwu, Wimmer, Greiml, (Stojković 62), Grahovac, Petrović (Ljubicic 81), Knasmüllner, Arase, Kara (Grüll 62), Fountas (Kitagawa 62).
Unused subs: Unger, Hedl, Ballo, Schick, Hofmann
Booked: Grahovac (43), Greiml (57), Diop (74).
Referee: Tobias Stieler (Germany).