Aubameyang opened Arsenal's scoring with a goal just five minutes in, while Ainsley Maitland-Niles made it 2-0 with a score of his own of an Aubameyang assist in the 15th minute.
Emery could have more transfer funds available if the Spanish head coach is able to steer Arsenal back into the top four in his first season in charge.
The Rennes boss Julien Stephan told this correspondent last week after the match at Roazhon Park in deepest Brittany that his team were facing a hard evening at the Emirates in the second leg.
The north London side will be hoping to overturn a 3-1 first leg deficit against Rennes in the return fixture at The Emirates in their Europa League last-16 tie on Thursday night.
Since then though he has positioned the team in fourth spot in the Premier League with eight games of the season to go.
"I missed two chances to close the game but, okay, most important we won today and we are all happy and proud".
After scoring Aubameyang donned a Black Panther mask to celebrate, and he explained why afterwards.
"We are going to think the same before every match".
Rennes pushed for an away goal but Aubameyang scored a third late in the second-half to seal Arsenal's progress.
After witnessing the 3-0 win against their Ligue 1 opposition, former Gunners striker Hartson told BT Sport: "Well they're in the quarter-final of the Europa League, where they've got an opportunity, if they do win it, of getting in the Champions League".
While Sokratis was forced to sit out the second leg, Arsenal were able to call on Alexandre Lacazette after his three-match ban for a red card in the previous round was reduced to two games on appeal and, having already served both of those games, so took his place in the side.
"On the offside, it was very clearly an injustice, it was an error", he said. "It's a learning curve for a club of our level, we don't have the power of Arsenal".