The forward struck four minutes before the break in Sweden to bag a crucial away goal and level the tie, after Vilde Bøe Risa had opened the scoring for Göteborg FC inside two minutes at the Valhalla IP.
Sam Mewis then marked her European debut with a goal to turn the game on its head with just under 15 minutes to go, handing the visitors a strong 2-1 advantage to take back to Manchester in a week's time.
City mounted an impressive comeback in difficult conditions on a bitterly cold evening in Sweden, to give us a crucial advantage going into the return leg in Manchester.
While City had reached the semi-finals of the competition in our first two Champions League campaigns, the last two seasons had proved disappointing with eliminations in the Round of 32 and 16 stages.
Since then, a quartet of European and World Cup Champions had joined the ranks with Mewis making her tournament debut, and Lucy Bronze and Alex Greenwood competing for the first time since lifting the trophy in August with Lyon – and City showcased that winning mentality to grind out a win.
The 2020/21 competition would pit City against the Swedish champions – the toughest possible test in Taylor's eyes; made more difficult with the combination of freezing temperatures and an artificial surface.
The game kicked off as the snow began to fall in Göteborg but fired up from the off, it was the hosts who drew first blood.
Putting the away side under immediate pressure, the home side won the ball back on the left flank and Anna Csiki drove at the City defence, skipping past Bronze and firing across goal. Pauline Hammarlund’s initial shot was well-saved by Ellie Roebuck but Boe Risa was on hand to convert the rebound.
The early setback rattled the visitors, who struggled to maintain a period of possession or carve opportunities out in the opening half-hour.
Kelly created our first half-chance, cutting inside and firing over and the effort sparked City into life.
Stanway then crashed an effort off the bar while Sunday's star, Caroline Weir, watched a low attempt suffer the same fate, before volleying just wide.
It would prove third time lucky, as City hit the woodwork for a third time but on this occasion, it bounced the right side and into the back of the net, as Stanway fired a low drive into the bottom corner, after Keira Walsh had regained possession in the centre.
With momentum, City came flying out of the blocks in the second half, as Stanway, Mewis, Kelly and Janine Beckie all tried their luck to no avail.
The second half was one-way traffic but the final product was found lacking.
There were excellent chances to snatch a win. Weir blazed over the bar – as did Csiki in a rare attack at the other end.
The magic moment arrived on 75 minutes when Weir (fresh from her trio of assists at the weekend) turned provider once more, clipping the perfect delivery into Mewis' path and the 'Tower of Power' headed back across goal and into the far corner.
The United States star almost added further gloss to the scoreline but two would be enough to secure the win, although Filippa Angeldal did almost grab a late equaliser.
How we lined up
CITY XI | Roebuck, Morgan, Greenwood, Houghton (C), Bronze, Walsh, Weir, Mewis (Coombs 84'), Beckie (Park 73'), Kelly, Stanway (White 73;).
SUBS | Bardsley, Benameur Taieb, Scott, Bonner.
GÖTEBORG | Falk, Kullberg, Koivisto, Roddar, Blackstenius (Ijeh 89'), Boe Risa (C), Curmark, Hammarlund, Angeldal, Csiki (Andersson 76'), Wijk.
SUBS | Geurts, Junttila Nelhage, Svegberg, Folds.
Player of the Match: Caroline Weir
She starred in the win over Everton on Sunday and once again, Caroline Weir produced an influential display.
At the heart of her side's best attacking moves, the Scotland international unlocked the Göteborg FC defence with another moment of quality to tee up Mewis for the winner.
Stanway's first half strike marked her 50th goal in all competitions for the Club.
Meanwhile, the game itself marked City's 100th away game (excluding those in neutral venues).
It's a crunch clash in the FA Women's Super League as City entertain second-placed Arsenal.
The heavyweights lock horns on Sunday 13 December in a 14:30 (UK time) kick-off at the Academy Stadium.
Champions League action then returns to the home of the FA Cup winners, as City host Göteborg in the Round of 32 second leg on Wednesday, 16 December (15:00 UK time).
Match highlights from the Vallhalla IP and a full 90-minute replay of the match (available with a CITY+ subscription) will be available from noon UK time on Thursday 10 December.