Miller took the chequered flag on Sunday – his first in MotoGP™ since the 2016 Dutch TT on a Marc VDS Honda – ahead of Bagnaia in second place.
In a race expected to favour Yamaha pace at Jerez, the Ducati duo defied the odds to seal the team’s first 1-2 in just under three years.
“I think I’m the happiest person in the world right now,” Dall’Igna said after the race.
“Jerez has always been a difficult track for the Ducati bikes, so to be able to finish first and second today is crucial for us, especially from a technical point of view.
“Both riders had a sensational race and were fantastic.
“They knew how to run a mature race – Jack kept a good rhythm and perfectly managed the race, while Pecco (Bagnaia) did an incredible performance, ending second and taking now the championship lead.
“Congratulations to both of them, to the team and all of Ducati Corse.”
Bagnaia leads the MotoGP™ standings on 66 points after four rounds of the 2021 season, while Miller is in sixth place overall.
“Today in the race, I felt really comfortable riding the Desmosedici GP bike, thanks to the great work done with my team over the weekend,” Bagnaia said.
“Today’s result is really incredible, and I hope we can continue like this in the next races, which will be held on tracks favourable to our bike.
“Tomorrow we will have another day of testing, so we have to stay focused.”
The 2021 MotoGP™ season continues in a fortnight’s time at the French GP in Le Mans.