The three-time Danish champions, who finished third last term, reached the second qualifying round by easing aside Romanian side Farul Constanța 6-2 on aggregate, while the 16-time Scottish champions hammered Athlone Town 6-0.
Both entered the game full of confidence and last season’s SWPL runners-up dominated the early possession, but they had rarely crossed the halfway line by the time Lee Gibson was forced into an 18th-minute double save.
The Scotland goalkeeper parried a powerful shot from on-loan Kansas City Current winger Flora Marta Lacho and then denied former Everton forward Rikke Madsen on the rebound.
Denmark international Madsen volleyed just over from edge of the penalty box, Lacho headed straight at Gibson, who then saved at Garcia’s feet, while fellow American full-back Macy Schultz headed just wide.
It was no surprise when the greater power and speed displayed by hosts honed by Scottish fitness coach Kieran McManus led to a 32nd-minute opener.
Denmark and former Crystal Palace midfielder Gejl, weaved inside a couple of challenges and fired in off the far post from 16 yards.
City, though, hit back nine minutes later with their first sojourn into the home penalty box.
Haley Lauder’s free-kick to the back post deflected into the path of fellow midfielder Anderson to stab home from inside the six-yard box.
However, on the hour mark, the visitors paid for hesitancy as they attempted to play out from the back as American midfielder Garcia pounced to fire home from just outside the penalty box.
Gibson then struggled to turn Jereko’s shot just over and, when the corner fell to the on-loan Kansas City midfielder, her excellent volley fizzed just wide.
City still had chances for a second equaliser and it was Ema Aleksić’s turn to make a double save, parrying a low drive from Nicole Kozlova and pushing fellow forward Sofia Maatta’s follow-up into the side netting.
Kozlova had another chance to score against her former club when the home goalkeeper failed to gather a pass back but was thwarted by a last-ditch challenge before it was Gibson’s turn again to block a Sarah Thygesen shot with her legs.