The Swedish striker netted from close range in the 93rd minute to seal a deserved semi-final win for the Gunners, who will now compete in the final for the ninth time.
While clear-cut chances on goal were relatively few and far between in the first half, Arsenal were presented with a golden chance to break the deadlock in the fifth minute through Laura Wienroither.
The right-back surged towards goal following a quick counter-attack, but Sandy MacIver got down low to save before both sides proceeded to largely cancel each other out.
New signing Sabrina D'Angelo was called into action in the 23rd minute, comfortably gathering Chloe Kelly's curling shot after the England international cut inside from the right and let fly.
The visitors provided most of the attacking threat as the first half wore on, but an explosive start to the second saw Caitlin Foord strike the bar in the 48th minute, but the offside flag had gone up anyway.
The Gunners continued to dominate the second half, and Jonas Eidevall rang the changes just after the hour mark, but one of his substitutes missed a glorious opportunity to give Arsenal the lead in the 66th minute.
A sumptuous ball to the back post from Katie McCabe was headed back down by Foord to Lina Hurtig, but the Swede inexplicably crashed the ball against the bar from a couple of yards out.
Eidevall's side continued to press for the winner, which nearly arrived from Blackstenius on the turn, but MacIver remained impenetrable and produced a smart save from Blackstenius's close-range effort in the 85th minute.
Just one minute later, Hurtig was guilty of another horror miss, as Foord whipped in a ball from the right which found the Swede in acres of space, but she got her header completely wrong and the ball trickled harmlessly out for a goal kick.
Arsenal's lack of ruthlessness would lead to extra time after a goalless 90 minutes, but for all of their profligacy in normal time, the Gunners finally broke the deadlock in the 93rd minute.
The two Swedish strikers in Hurtig and Blackstenius combined, as the latter fed a ball in from the left for her teammate to slot home from close range, aided by a final touch from City substitute Leila Ouahabi.
Arsenal survived one final scare when Hayley Raso failed to connect properly with Ouahabi's cross to the back post in the 120th minute, as the five-time winners set up a final showdown with West Ham United or Chelsea, who compete in their semi-final on Thursday.