Arsenal exploited City's high defensive line - and lack of pace the back - by playing through passes either side of central defenders Rebecca Knaak and Jade Rose.
Smith beat Knaak to a Mariona Caldentey pass before rounding Ayaka Yamashita and slotting into the empty net, but originally that job was not meant to be her's.
Stina Blackstenius picked up a calf issue during the week, forcing manager Renee Slegers to find an alternative solution.
"We have been successful with Stina [Blackstenius] in the nine, she is so good with her physicality and speed," said Slegers.
"She wasn't available, so we wanted similar qualities even though Olivia and Stina are very different players. Liv [Smith] had two-and-a-half training sessions in the nine position.
"[There was] a lot of meetings with coaches, giving her the details without putting too much information in her head so she could play on intuition, because that is when she is really good.
"She picked up the role brilliantly, the goal was exactly what we wanted."
Of course, opponents rarely employ defensive lines against Arsenal as high as City did, but the Canada forward showed she can be relied upon.
"We have different options [for different opponents]. This was very specific for us today, Olivia hasn't done it for us before. But she performed really well, so of course we will see her as an option going forward."
It's easy to forget that Smith has been playing in the WSL for less than two years.
After developing in Portugal with Sporting CP, one season at Liverpool was enough to convince Arsenal to spend big.
"There is more to come – she is still a young player, she is settling in the environment," said Slegers.
"It's been a while now, but don't underestimate what it takes for a player and her situation to settle and adjust to a new life.
"She's great to work with, her ability on the pitch is so good. She helps the team with her specific qualities, but she's also a pleasure to work with. She is making small steps but she is at a really high level."
Smith let her team-mates down by getting sent off during the League Cup semi-final defeat by Manchester United last month, but she has bounced back in a serious way.

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