Bonucci scored for the hosts from close range in the 47th minute after Inter's Danilo D'Ambrosio made a horrid mistake by heading Paulo Dybala's free kick across his own goal.
Substitute Morata added the second goal from the penalty spot after being tripped by Joao Miranda with six minutes to go.
Juve now have 61 points from 27 matches, four more than second-placed Napoli who travel to Fiorentina on Monday, and remain on course for a record fifth consecutive 'Scudetto'.
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"We absolutely had to win," Bonucci told Italian television. "Two consecutive draws would have been too many, we had to win to send out a message.
"We haven't put pressure on Napoli, we are the leaders so
we only care about our own results."
Roberto Mancini's inconsistent Inter are fifth on 48 points, four behind fourth-placed Fiorentina and five adrift of AS Roma who are third.
After defeating title rivals Napoli 1-0 on Feb. 13, Juve's club record 15-game winning streak was halted by last weekend's draw with Bologna.
Massimiliano Allegri's men dominated the opening stages on Sunday with Dybala, Mario Mandzukic and former Inter midfielder Hernanes going close in the first 45 minutes.
The visitors adopted a defensive approach and fell behind after Bonucci's far-post finish. Morata then made it 2-0, two minutes after coming on to the field.
"We now have one less obstacle on our road to the title," said Allegri. "The more games we win, the less we will still have to do."
The sides meet again in Milan on Wednesday in the second leg of the Italian Cup semi-final, with the league leaders holding a 3-0 advantage.
(Writing by Ed Dove; Editing by Tony Jimenez)
