Second seed Federer had to deal with a tricky opponent and strong gusts at the Aviation Club in front of nearly 5 500 fans at the Aviation Club, needing all three sets to make it past the opening round.
The Swiss, a seven-time Dubai champion, had to go up a gear in the third set to advance to a second round meeting with Fernando Verdasco after German Kohlschreiber made a match of it by winning the second.
"I'm just happy to get through, it was tricky conditions out there," the 20-time Grand Slam champion said after his 14th straight win over Kohlschreiber, his friend and practice partner.
"Philipp caused me a lot of trouble and we played in swirly conditions. All of a sudden it (the wind) could stop and you could be a break down. That also plays in your head a little bit.
"I know the game's there. It was just really difficult conditions tonight."
Federer, who is seeded behind Kei Nishikori, swept the opening set after breaking in the first game but was pegged back.
Kohlschreiber, ranked 31st in the world, made a match of it in the second, breaking Federer three times on his way to taking the set 6-3.
The final game of the set was a nine-minute thriller, with the Swiss seed saving three set points before Kohlschreiber levelled the match with a volley winner.
But Federer cruised to the third set and the next round.
READ: Khachanov, Raonic suffer early exits in Dubai
Earlier, seeds Karen Khachanov and Milos Raonic suffered surprise first-round exits in testing conditions.
Georgian Nikoloz Basilashvili stunned Russian fourth seed Khachanov 6-4, 6-1, while world No 14 Raonic was beaten his Dubai debut 6-4, 5-7, 6-4 by German Jan-Lennard Struff.
Khachanov went down in just 69 minutes to 19th-ranked Georgian Basilashvili, winner of two titles last season, as winds played havoc during the day.
"I know Karen is not having his best time at this moment. But I also did not have great beginning of the season," said Basilashvili.
"I was able to manage my nerves just (for the) whole match, especially in the windy conditions. It was really tough, (and I'm) really happy for sure."
Raonic battled for more than two hours but was unable to get past Struff.
In an unusual incident, one of Raonic's rocket serves struck a ball girl straight in face.
After a five-minute pause for treatment, she was led off court by a first-aid worker - the girl returned at the end of the match and shook hands with the player, who gave her a racquet.
The Canadian fired 15 aces in his losing effort, dropping serve twice.
Struff advanced into a second-round match with Marton Fucsovics after the Hungarian defeated Damir Dzumhur 6-1, 7-6 (7/5).
Former finalist Verdasco smashed 13 aces as he put out Italy's Thomas Fabbiano 3-6, 6-3, 6-2.