Bogdanovic is trying to break into the world's top 100

The pair will meet in round two after Bogdanovic beat former semi-finalist Hyung-Taik Lee 6-4 6-4, and Baker saw off Alexander Peya 3-6 7-6 (7-5) 6-3.

Fellow Briton Richard Bloomfield went down 6-4 6-2 to Robby Ginepri, and Max Mirnyi beat Fernando Verdasco 6-3 6-3.

"I just tried to stay as aggressive as possible," Bogdanovic told BBC Sport.

Queen's highlights: Bogdanovic beats Lee

"This is a great opportunity to play good players and every match I win will help me move forward. When I break the top 100 it will be tough playing players like this every week."

Wild card Bogdanovic, 23, is ranked 70 places below 13th seed Lee at 117th in the world.

Baker, another wild card and ranked 247, fought back from a set and a break down against Peya to claim the first ATP Tour win of his career.

"It definitely will help me push on because that's the first top-100 player I've beaten, obviously at a fairly big tournament," said the Scot.

"The fact that I was able to just hang in there - I was 6-3 5-3 down and I gave myself a chance to just work things out - was the most positive thing for me."

And on a good day for the home nation, Jamie Murray and American Eric Butorac won their first-round doubles match against Ivan Ljubicic and Ernests Gulbis 6-1 7-6 (7-1).