There was an expectation that Sonia Bompastor's team would make light work of the Austrian side making their first-ever appearance in the competition proper, but this was a far tighter, far more competitive match-up than had been anticipated.
Wieke Kaptein scored after 11 minutes with a lovely effort that skimmed the underside of the bar on its way in, and at that stage it looked as though the floodgates would open.
But Vienna dug in, not only holding off their far more expensively assembled opponents but taking the game to them and leaving the hosts relieved to escape with a victory, particularly after Kosovan forward Modesta Uka had struck the post late on.
Chelsea went ahead in spectacular style early on when Kaptein hammered it in off the bar from 25m out.
Carpenter spurned a golden chance to make it two when she scuffed a shot wide of the near post, then Alyssa Thompson's powerful run down the right ended with her slamming an effort across goal and wide.
Keira Walsh was forced off injured after 20 minutes in a potential blow for Chelsea ahead of Sunday's WSL game at home to Arsenal.
There was almost a sublime equaliser on Wednesday night (Thursday AEST) when Louise Schoffel danced her way through Chelsea's defence and hit a low shot that flashed inches wide of the post.
Sjoeke Nusken should have settled the match and her manager's nerves with a free hit 10 yards out that she wastefully thumped into the supporters behind the goal from Carpenter's cross.
Chelsea's number looked to be up when Uka went through and hit the post, but they clung on for a nervy win.
Elsewhere, Marie-Antoinette Katoto scored a hat-trick as Lyon thrashed Servette 8-0 in their opening game of the WCL.
Katoto's treble alongside Melchie Dumornay's brace and two own goals from the Swiss side helped Lyon accelerate to the top of the standings with a crushing display.
Ewa Pajor's brace helped holders Barcelona get off to winning start as they beat Paris FC 5-2.
The defending champions were handed an initial scare when Evelyne Viens put Paris in front only five minutes in, but Kerolin replied for the hosts.
Clara Serrajordi put Barca ahead in the 28th minute, kicking off a destructive 15 minute-period for the hosts, in which Pajor and Caroline Graham Hansen struck.
Pajor struck again in the 70th minute and Paris then pulled one back through Clara Mateo as Barca comfortably saw out the win.
OH Leuven and Roma played out a goalless draw in their clash.
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