The Swiss top seed, playing the event for the second time after winning the title on his debut in 2008, lifted his spirits as his French Open title defence draws nearer.
"I got off to a bad start in the first game, down love-30, he played a great passing shot to start," said Federer.
"I looked for my forehand too much. The next thing you know, you are down love-40. He got me on the back foot and I had to play careful. I missed some chances and made too many mistakes in the first set.
"It was not beautiful tennis from my side."
Federer will on Saturday compete for a spot in his second final at the Estadio Nacional in a match against holder Albert Montanes, after the fourth-seeded Spaniard defeated number eight seed Pablo Cuevas 6-4, 6-3 in their quarter-final.
At the bottom of the draw, fifth seed Guillermo Garcia-Lopez of Spain advanced when compatriot Alberto Martin retired with a stomach complaint when trailing 6-0, 2-0.
Federer kept a perfect record of 7-0 at the tournament after defeating former Top 10 player Clement, now ranked 83rd, in their first meeting in four years.
Federer leads 7-3 in the series against the man who stopped him twice at the Australian Open early in his career, having won their last six matches.
The opening set under cloudy skies and amid chill temperatures was combative, with Federer needing to come back from a break in the opening game, which he got back in the fourth for 2-2.
He still required 68 minutes to win the opener in a tiebreak, though, after saving a Clement set point.
Once the initial hard work was done, Federer lifted his game in the second set, finding his range and going up two breaks.
The world number one took home the victory on his second match point after just over 90 minutes.
"In the second set I could open up a bit and take a few chances, I learnt from the first set," said Federer, recovering his form after an opening-round loss last week in Rome. "I was finally able to put him away.
"Arnaud is tough, I've always struggled with him. He knows what I like and what I don't like so much."
On the women's side of the draw, Anastasia Sevastova of Latvia and Spaniard Arantxa Parra Santonja will play for the title after Sevastova beat Chinese seventh seed Peng Shuai 6-7 (6/8), 6-1, 6-3 and Santonja upset second seed Sorana Cirstea 6-1, 6-4.
"The first set was a battle and I knew that I would have to step it up," said Sevastova, the number 74 who made the semi-finals this spring in Monterrey, Mexico.
"I played more aggressive, put pressure on her and that helped. I'm happy to be in the final, it's amazing."