In a frantic first half which featured three goals in nine minutes, Paralluelo latched on to Caroline Graham Hansen's cross at the back post to put Barca ahead.
Bayern equalised when Harder drove forward on the counter-attack before laying off for Dallmanto to score with a first-time finish.
Barca restored their advantage through Putellas, who finished from inside the penalty area after Vanessa Gilles failed to clear.
Pajor converted Paralluelo's cross from the left and Putellas acrobatically volleyed in after Esmee Brugts' header from a set-piece.
Harder capitalised on poor defending to pull a goal back for Bayern, before substitute Arianna Caruso had an effort tipped on to the crossbar by Barca keeper Catalina Coll, and Dallman hit the bar moments later.
Harder netted for a second time in stoppage time, only for the goal to be disallowed for a foul in the build-up.
Barca midfielder Aitana Bonmati, the winner of the past three Ballons d'Or, came on as a second-half substitute, her first appearance since breaking a leg in November.
"I'm so happy to be back. We make it to another final," she told ESPN.
"Our team is doing an amazing season. Another Champions League final. Incredible team.
"In my career I've had very special moments but today is one of the most special moments. Back from a long injury in front of 60,000 people and beating Bayern is special."