Rossi set the early pace on his factory Yamaha with a 1m39.881s, though this was immediately bested by Maverick Vinales with a 1m39.655s.
Morbidelli then took over top spot with a 1m39.110s to end the first runs fastest, while teammate Quartararo was only seventh after making a mistake on the way into Turn 10.
As the session entered its final few minutes, it was the Yamaha quartet lighting up the timing screens, with Quartararo edging ahead with a 1m39.008s.
But Morbidelli dug deep on his final lap and monstered the final sector of the Catalunya circuit to fire in a 1m38.798s to claim his first pole in the premier class and his first in grand prix racing since his final Moto2 season in 2017.
Quartararo went for one final lap just as the chequered flag came out, but was unable to improve on second, with Rossi completing the front row for the first time this season.
Pramac’s Jack Miller was the best Ducati runner in qualifying in fourth, the Australian’s 1m39.225s coming early in Q2 on his only soft tyre run having had to use up an extra one to come through Q1.
Joan Mir could only manage eighth on his Suzuki, with Danilo Petrucci on the works Ducati and KTM’s Brad Binder completing the top 10.
LCR’s Takaaki Nakagami could only go 11th on his year-old Honda after progressing from Q1, with Miguel Oliveira 12th on the Tech 3 KTM after an early fall at Turn 10.
Dovizioso’s tough season continued, as the Ducati rider failed to get anything going in Q1 and could only produce a 1m40.109s good enough for 17th on the grid.
Marking the third time he hasn’t escaped Q1, Dovizioso will start alongside Honda’s Alex Marquez in 18th and the injured LCR Honda of Cal Crutchlow in 16th.
Alex Rins came close to getting into Q2 to join teammate Mir, but was denied by Nakagami at the end of Q1 and will start 13th ahead of Francesco Bagnaia (Pramac) and Aprilia’s Aleix Espargaro.
|1|| Franco Morbidelli ||Yamaha||1'38.798|
|2|| Fabio Quartararo ||Yamaha||1'39.008||0.210|
|3|| Valentino Rossi ||Yamaha||1'39.129||0.331|
|4|| Jack Miller ||Ducati||1'39.225||0.427|
|5|| Maverick Viñales ||Yamaha||1'39.371||0.573|
|6|| Johann Zarco ||Ducati||1'39.378||0.580|
|7|| Pol Espargaro ||KTM||1'39.495||0.697|
|8|| Joan Mir ||Suzuki||1'39.628||0.830|
|9|| Danilo Petrucci ||Ducati||1'39.641||0.843|
|10|| Brad Binder ||KTM||1'39.659||0.861|
|11|| Takaaki Nakagami ||Honda||1'39.713||0.915|
|12|| Miguel Oliveira ||KTM||1'40.188||1.390|
|View full results|
|1|| Jack Miller ||Ducati||1'39.399|
|2|| Takaaki Nakagami ||Honda||1'39.547||0.148|
|3|| Alex Rins ||Suzuki||1'39.751||0.352|
|4|| Francesco Bagnaia ||Ducati||1'39.777||0.378|
|5|| Aleix Espargaro ||Aprilia||1'39.973||0.574|
|6|| Cal Crutchlow ||Honda||1'39.988||0.589|
|7|| Andrea Dovizioso ||Ducati||1'40.109||0.710|
|8|| Alex Marquez ||Honda||1'40.164||0.765|
|9|| Iker Lecuona ||KTM||1'40.490||1.091|
|10|| Stefan Bradl ||Honda||1'40.721||1.322|
|11|| Bradley Smith ||Aprilia||1'40.838||1.439|
|12|| Tito Rabat ||Ducati||1'41.013||1.614|
|View full results|