Federer was too good for his opponent even though the 75th-ranked Argentine produced one of his best matches on grass.
With the Swiss great serving for the match, Pella forced two break points for some late drama. But Federer answered with four points in a row to set up a meeting with Nick Kyrgios.
``I didn't give Guido many chances to get into my service games, except maybe the last couple,'' Federer said after only his second match since March 24. ``I was happy that I also got more rhythm today.''
The fourth-seeded Kyrgios defeated Feliciano Lopez 6-4, 3-6, 6-3.
Federer can reclaim the No. 1 ranking from Rafael Nadal with a win on Saturday.
``In the match that you play for world No. 1, it's clearly going to be in the back of your head,'' he said.