Joshua, the former world heavyweight champion, had lost his last two fights against Oleksandr Usyk and was looking to make a statement with a convincing win over Franklin.
After 12 rounds, Joshua was awarded a unanimous points decision victory with the three judges scoring the fight 118-111, 117-111, and 117-111 in favour of the Briton.
"It was important to win," Joshua said.
"Jermaine has a good duck and dive style, somebody else from Britain will probably knock him out; respect to him, he did well.
"I should have knocked him out but it is done. On to the next. He is here to prove himself, not roll over. I wish I could have knocked him out."
Despite repeatedly landing with his left jab and several powerful rights, the American challenger Jermaine Franklin went the distance, "He is here to prove himself, not roll over."
However, Joshua's hand was raised in victory, earning his 25th win in 28 professional fights and keeping alive his hopes for a "Battle of Britain" clash with WBC heavyweight champion Tyson Fury.
"I try and provide for the fans," said Joshua.
"They said Tyson Fury; the ball is in his court. I would be honored to fight for the WBC heavyweight championship of the world. We ain't getting any younger."
Although Joshua landed several powerful right-hand punches, he had to work hard against Franklin, who showed great resilience throughout the fight.
A bizarre end to the fight saw Joshua push his head into Franklin before the 12th round appeared to end eight seconds early.
Lorenzo Adams, Franklin's strength and conditioning coach, responded with an angry reaction towards Joshua. The corners and fighters clashed momentarily before security intervened to calm the situation.
Security intervened quickly, and Joshua's hand was lifted in victory for the 25th time in his professional career.
This victory keeps alive Joshua's hopes of a Battle of Britain against WBC champion Tyson Fury.
With this win, Joshua has put himself back in contention for a title shot and will be hoping to build on this performance in his future fights.