Edmund, ranked 46th in the world, needed just 65 minutes to get past the 95th-ranked Elias and line up a third career meeting with Djokovic, a five-time winner at Indian Wells who is seeded second this year behind world number one Andy Murray of Britain.
"The things (Djokovic) does well are making a lot of balls and being quick around the court. It's tough to get the ball by him and break him down," said Edmund, who lost to the Serb star at the Miami Masters and US Open last year. "These are things that I've experienced the last two times I've played him. I'll try and use that on Sunday."
After a lackluster end to 2016 that saw him surrender the world number one ranking to Murray, things appeared to be looking up with his victory in Qatar in January.
But a shock second-round exit at the Australian Open followed by a quarter-final loss in Acapulco have him back in rebuilding mode.
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With 32 seeded players enjoying first-round byes, it was unseeded players jockeying for position on Friday.
US 19-year-old Taylor Fritz dispatched France's Benoit Paire 6-3, 6-2 to line up a meeting with third-seeded Croatian Marin Cilic.
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Fritz, a Southern California native, kept his focus as injury contributed to some erratic play from Paire.
"My focus was just to serve, serve well, kind of just manage my service games, because I felt like I would get chances on his serve and I would just have to take them," said Fritz, who saved the only break point he faced in the 65-minute match.
"It was just a weird match, because the ankle or foot injury or issue he had in the beginning -- sometimes he'd move really well, sometimes he wouldn't. Sometimes he would just double fault, sometimes he'd hit an ace."
In addition to adjusting to full-time life on the tour, Fritz has been through momentous personal changes. He's a married father of an infant son, still trying to map his burgeoning career.
While he finds time spent with his son "amazing," Fritz is the first to admit that his wife, Raquel, is doing the heavy lifting when it comes to childcare.
"I'm not very hands-on at all, to be honest," he said.
"We're both pretty serve dependent," he said. "So I will be focusing on the key parts of my game, which is the serve and just staying aggressive, attacking, but not giving him too many free points."
In other matches, France's Stephane Robert defeated Israeli Dudi Sela 6-4, 6-4 to book a meeting with ninth-seeded Roger Federer, a four-time Indian Wells winner who is riding high after capturing his 18th Grand Slam title at the Australian Open.