It took until the 55th minute for the deadlock to be broken by Pajor, but Barcelona ran away with the game after that at the Ullevaal Stadion in the Norwegian capital.
Polish striker Pajor put the pain of five previous final defeats behind her as she also scored her team's second goal on 69 minutes, leaving Lyon with too much to do.
Pajor was on the losing side in four Champions League finals with previous club Wolfsburg before joining Barcelona in 2024 and playing in their 1-0 loss to Arsenal in Lisbon last season.
Spain World Cup winner Paralluelo then added two late goals as Lyon fell apart, exposing a gulf between the two outstanding club sides in women's football over the last decade.
The victory, and manner of it, confirmed that Barcelona have overtaken Lyon as the dominant force in recent years, as they won their fourth title, all of which have come in the last six seasons - only Lyon, with eight, have won more overall.
Barcelona's European triumph follows a clean sweep of the Spanish domestic honours, and the Catalans brought reigning Ballon d'Or Aitana Bonmati on as a second-half substitute here following her recent return from a broken leg.
This was a sixth straight Champions League final appearance for Barcelona, and their seventh in the last eight seasons.
They had already beaten Lyon 2-0 in the 2024 final, when Bonmati and Alexia Putellas scored their goals - the latter wore the captain's armband here in what could turn out to be her farewell appearance with her contract now up.
This was the fourth time the clubs had met in the final, with Lyon coming out on top in 2019 during their run of five consecutive titles, and also winning in 2022 - but that is now the only time they have lifted the trophy in the last six editions.
Ada Hegerberg scored a hat-trick in the 2019 final and was also on target three years later, but the competition's all-time leading scorer looked a shadow of her former self on this occasion, which was a homecoming for the Norwegian former Ballon d'Or winner.
Barca storm to emphatic win
Lyon must now try to lift themselves for a French title decider against Paris FC next weekend, after failing to go the extra step in Europe following their defeat of reigning champions Arsenal in the semi-finals.
The French side thought they had taken an early lead in the evening sunshine in front of a crowd of 24,258, with Lindsey Heaps converting the rebound after a Wendie Renard header had been saved by goalkeeper Cata Coll.
However, the effort was disallowed for offside following a VAR check.
Barcelona perhaps should have scored soon after as a mix-up between Renard and Lyon goalkeeper Christiane Endler allowed Pajor to try a lob from outside the area, but her attempt hit the side-netting.
Coll saved well from a Selma Bacha free-kick as the first half ended goalless, but Barcelona looked the more likely side and were rewarded with the opener 10 minutes after the restart.
Patri Guijarro was the creator with a driving run and pass to Pajor, who controlled, took another touch to steady herself, and fired in.
Coll tipped a Vicki Becho shot around the post as Lyon sought a leveller, but instead Barcelona increased their lead just past the midway point in the second half.
The French champions failed to clear the ball in their box, and Paralluelo cut it back from the byline for Pajor to score.
Substitute Tabitha Chawinga's inability to beat Coll when clean through summed up Lyon's evening, and Paralluelo added a late brace to make it an emphatic victory.
Her magnificent rising strike from range in the 90th minute was the pick of the goals on the day, before she ran through to make it 4-0 in stoppage time.
