The Indian F1 team is now trailing fourth-placed Williams by just one point at 19 as Julkenberg collected 10 points with his stupendous effort after starting seventh from the grid.
Perez failed to start the race after suffering a series of issues, which caused the car to get stuck in gear on the way to the grid.
"Today was a super team effort and I'm very happy with fifth place. We were the only team among the frontrunners to do a two-stop race and we had good pace all afternoon. It shows that the team's hard work over the winter is paying off and it feels great to be so competitive and fighting up at the front," Hulkenberg said.
Perez said he was disappointed not to have a chance to race today.
"We are still investigating the cause of the problem but the car kept going into neutral when I was downshifting on the way to the grid. I made it back to the garage but we could not find a solution. I need to focus on the positives because we learned a lot from the weekend so I hope we can come back stronger in Bahrain," he said.