The French driver, an impressive fourth at Sakhir last weekend for the Honda-powered Italian Formula One team, finished last but one in Shanghai while New Zealander Hartley retired with gearbox damage.
Stewards added 10 seconds to Gasly's time at the finish and also gave him two penalty points, his first in Formula One, for an incident the team put down to miscommunication.
"I apologise to Brendon for the contact we had, the team told me that they were going to switch our positions so I went on the inside of the back straight thinking he would give me space," said Gasly.
"Unfortunately I don't think he saw me and once I was inside there was nothing I could do," added the rookie, who was awarded 'Driver of the Day' for his race in Bahrain.
The incident scattered debris across the track, bringing out the safety car, with Gasly suffering a broken front wing and bent steering.
Hartley, who has yet to score a point since his debut late last year, had started near the back and was struggling on the ultrasoft tyres.
"I think the accident with Pierre was down to a miscommunication," he said.
"The team asked us to swap positions because we were on completely different strategies, so I was going to let him by on the exit of turn 14 like I did at the start of the race."
(Writing by Alan Baldwin in London, editing by Toby Davis)
