The defending champions had never beaten the French giants, losing in the 2019 and 2022 finals against them, but finally succeeded in Bilbao to compete a spectacular quadruple this season in coach Jonatan Giraldez's last match in charge.
Bonmati pounced after 63 minutes and substitute Putellas finished the job in stoppage time to avenge Barcelona's prior defeats by Sonia Bompastor's side.
Securing their third Champions League trophy from five final appearances across the last six seasons, Barcelona demonstrated that they are the new powerhouse of the women's game.
Barca stars insisted this time they were capable of beating Lyon, adding experience and mental strength to their undoubted talent, and so it proved at a packed San Mames.
Backed by the vast majority of a 51,000 record crowd at a women's Champions League final, Bonmati and her side completed one of the few outstanding challenges remaining to them.
"It's the first time we've beaten Lyon, I'm proud of the team, and we know that with these fans we have, we can't fail," Bonmati told DAZN.
"It's incredible what we're living through as a team, I'm so lucky... to see we're creating that for so many people, the historic amount of fans we've brought, it's the proudest I've felt, I wouldn't change it for anything."
Giraldez started Mariona Caldentey in attack and moved Fridolina Rolfo to left-back, dropping Ona Batlle to the bench alongside two-time Ballon d'Or winner Putellas.
Lyon left Ada Hegerberg on the bench too, with the all-time top scorer in the competition's history struggling for form after injury.
Lucy Bronze deflected a ball onto her own crossbar and Lyon's towering captain Wendie Renard hit the outside of the post as Barcelona suffered a couple of early jitters.
After going four goals down by half-time in the 2019 final and three down in 2022, this time the Catalans dug deep to hold it together at the back.
Breakthrough
Barca threatened increasingly at the other end. Patri Guijarro, who scored twice in last year's final against Wolfsburg, broke in behind for their first big chance after half an hour.
Christiane Endler saved her effort from an angle and Selma Bacha cleared the ball off the line after it rebounded back towards goal.
Caroline Graham Hansen, in sparkling form this season, gave left-back Bacha a torrid time and had 11-time finalist Renard uncertainly backpedalling fearfully near the end of the first half, but dragged her shot wide.
Barcelona made their quality count after the hour mark when Bonmati sent them ahead.
The Ballon d'Or winner had been quiet but arrived just at the right time to collect Caldentey's clever pass and burst into the area.
Bonmati's low shot deflected off Vanessa Gilles and flew over the helpless Endler, for her sixth goal of the tournament and the most crucial.
Champions League top goalscorer Kadidiatou Diani curled agonisingly over for Lyon as Bompastor's side tried to fight back. Hegerberg headed off target as Lyon's chances ebbed away.
Eventually Putellas, on as a late substitute, put on the captain's armband and settled the game by rifling into the top corner to get Barcelona's celebrations started early.
