Enzo Maresca's side entered the clash with a two-goal advantage from the first leg, with Christopher Nkunku and Noni Madueke registering in the reverse fixture at Stamford Bridge.
Chelsea finished the job on Thursday, with Nkunku making the breakthrough from the penalty spot in the 14th minute after Mykhaylo Mudryk had been fouled by Keigo Tsunemoto inside the box.
Servette levelled the scores at 1-1 on the night in the 32nd minute through Jeremy Guillemenot, before the hosts made it 2-1 in the 72nd minute when Enzo Crivelli headed a cross from Timothe Cognat into the back of the net.
The Swiss outfit then went in search of a third, as they attempted to complete an incredible turnaround, but Chelsea managed to navigate their way through the final stages to advance to the group stage.
The Blues finished sixth in the Premier League last season, which was due to see them take part in the group stage of the 2024-25 Europa League, but Manchester United's success in the FA Cup final meant that the capital outfit had to settle for a spot in the playoff round of the Conference League.
It was far from a convincing performance from Maresca's team in Switzerland, but they managed to get the job done courtesy of a 3-2 aggregate success to secure their progression to the group stage.
SERVETTE VS. CHELSEA HIGHLIGHTS
14th min: Servette 0-1 Chelsea (Christopher Nkunku)
Chelsea make the breakthrough in the 14th minute of the contest, with Nkunku finding the back of the net from a penalty spot after Mudryk had been fouled by Tsunemoto.
The Premier League side take complete control of the playoff tie.
32nd min: Servette 1-1 Chelsea (Jeremy Guillemenot)
Guillemenot levels the scores against Chelsea on the night, with the collecting a pass from Dereck Kutesa before picking out the bottom corner. Servette give themselves a slight hope of a comeback in this contest.
72nd min: Servette 2-1 Chelsea (Enzo Crivelli)
Servette take a 2-1 lead on the night, as Crivelli heads a cross from Cognat into the back of the net. The home side are right back in this tie, with Chelsea struggling to get going after making the breakthrough.
MAN OF THE MATCH - TIMOTHE COGNAT
Cognat was the star of the show on Thursday evening, with the 26-year-old putting in an excellent performance for his side.
It was his cross that Crivelli headed into the back of the net to send the hosts 2-1 ahead on the night, and he continued to look dangerous when he had possession in the final third of the field.
Cognat was also more than prepared to help out his defence when required, and he was a key contributor to Servette recording what was an impressive result on the night despite the disappointment of the overall score.
SERVETTE VS. CHELSEA MATCH STATS
Possession: Servette 32%-68% Chelsea
Shots: Servette 14-8 Chelsea
Shots on target: Servette 3-8 Chelsea
Corners: Servette 6-5 Chelsea
Fouls: Servette 7-8 Chelsea
WHAT NEXT?
Chelsea will be bidding to make it back-to-back wins in the Premier League when they continue their domestic campaign at home to Crystal Palace on Sunday afternoon.
Servette, meanwhile, will look to put the European disappointment behind them when they also return to domestic action on Sunday, facing a trip to Winterthur in the Super League.