Chelsea forward Mayra Ramirez found the net in the first half, but her strike was ultimately ruled out due to a handball infringement.
After the respective goalkeepers were forced to make important stops in a cagey second period, the final was paused in stoppage time after Arsenal midfielder Frida Maanum worryingly fell to the ground off the ball.
The final drifted into extra-time following a lengthy period of treatment, before Arsenal ultimately found the decisive breakthrough, with Blackstenius scoring in the 116th minute to clinch the silverware.
Jonas Eidevall's have now won the Women's League Cup in back-to-back seasons, while the Blues have now lost five consecutive finals in the competition.
Chelsea made a positive start to the contest, with Lauren James registering a shot on target in the opening 10 minutes.
The England international shifted the ball onto her right foot, before forcing Manuela Zinsberger to push the shot away from danger.
As the final moved past the 20th-minute mark, the Blues thought they had taken a precious lead through January signing Ramirez.
The Chelsea forward picked out the bottom corner with a driven strike from outside the box, only to see her effort ruled out for Cuthbert's handball in the build-up.
After being put under pressure in the opening quarter, Arsenal offered their own attacking threat, with Cloe Lacasse firing straight at the resolute Hannah Hampton.
With the game finely poised for the break, the first meaningful chance of the second period fell to Lacasse in the 66th minute.
Arsenal won the ball back just inside their own half and quickly worked it to Lacasse, who drove into the box before drawing a fine save from Hampton.
As the contest entered the final stages of regulation time, it was Zinberger's turn to make a crucial stop in a cagey final.
The Switzerland international came out of the goal to narrow the angle and deflect James' right-foot strike wide of the far post.
There was then concern around Molineux when Arsenal's Maanum went down off the ball in stoppage time, resulting in a lengthy stoppage for the Norwegian to be tended to by the paramedics and physios before being stretchered off.
Understandably, the encounter petered out when the players returned to the pitch, ensuring another 30 minutes were required.
Arsenal began to take control in extra-time as Chelsea started to feel the effects of their midweek Champions League outing against Ajax.
Blackstenius blazed over from a promising position, before defender Kadiesha Buchanan made a last-ditch block to deny Caitlin Foord.
However, Arsenal's pressure ultimately paid dividends in the 116th minute when Foord laid the ball off to Blackstenius, who managed to squeeze her effort past Hampton to guide the record winners to their seventh Women's League Cup trophy and quash Chelsea's hopes of winning the quadruple in Emma Hayes's final season in charge.