Against an admittedly uninspired Vesely, Baghdatis had all the answers. He varied the pace on the ball, regularly hit the lines and showed some superb touches at the net.
"Now I play more with experience, more with the mind," said the 31-year-old Baghdatis.
"When you are young you just go out there and hit all the balls and [with] no fear so you don't think so much. Nowadays you have to think a bit more, try to find different ways of confusing the opponent and I'm doing that right now."
There is a special energy when Bagdahtis is on court, as you never know what might happen next. It's easy to understand why his matches in Melbourne over the years have been sellouts - regardless of his ranking - as fans flock to see the showman.
"I'm happy whenever the crowd likes the match that we give out there," said Baghdatis.
"That's very important. I play for that...I play for the crowd, I play for those emotions that the crowd give you when you make a winner, win a match or make an ace."
"You don't think about entertaining the crowd - it just comes naturally. They like the way you are, they like the person you are, they like what they see and I guess it is as simple as that."
Baghdatis will face Joao Sousa tomorrow, the in-form Portuguese who has yet to drop a set in the tournament. After going winless from three previous visits, the world No 43 has been in great touch this time and eliminated Robin Haase 6-3 6-2 today.
"The crowd is great," said Sousa. "The centre court is one of the nicest 250 [tournaments] I have played in. It's very comfortable to play and I feel very good."
In 2013 Sousa became the first Portuguese player to win an ATP event and joked yesterday that he is "very famous...in my home city".
Steve Johnson upset compatriot John Isner 6-3 5-7 7-6 (3) in another quarter final today.
The local highlight of the day saw Kiwi Artem Sitak and American partner Nicholas Monroe win through to the doubles semifinals.
They beat Argentinean combination Facundo Bagnis and Diego Schwartzman 3-6 7-6(5) 11-9 in a brilliant comeback that sparked jubilant scenes on the grandstand court.
"We knew we were going to have to come up with some good shots to beat them and we weren't really producing any of those, we were down a set and a break and we needed to do something," said Sitak. "That game where we were 3-2 down [and we broke back], that was a big momentum switch for us, and for the crowd, because they felt like we could actually do it."
