The Real Madrid attacker found the back of the net with a stunning strike in the 65th minute of the clash against Georgia to help Turkey record a 3-1 victory in their first match in Group F.
Guler netted six times in 12 appearances for Real Madrid last season, and the 19-year-old is being tipped to be one of the breakout stars of this summer's European Championship.
The forward revealed his delight after the final whistle and said that he had been practising his technique on the strike that ended up in the back of the net.
"I am just thrilled, no words to describe how I feel. I was dreaming of this goal constantly," Guler told reporters after the contest. "I've been practising this particular shot recently at the end of training sessions. I'm so happy to have scored this way.
Guler proves to be Turkey's star against Georgia
"My coach had wanted a goal as a birthday present. I hope I can continue these goals."
Georgia gave a strong account of themselves in Tuesday's contest, with Georges Mikautadze levelling the scores in the 32nd minute after Mert Muldur had sent Turkey ahead.
However, Vincenzo Montella's side went on to score twice more, with Guller sending the Crescent-Stars ahead in the 65th minute, before Kerem Akturkoglu netted a third for Turkey in the final exchanges.
Despite the disappointment of the defeat, Georgia head coach Willy Sagnol said that his side could be proud of their performance in their first-ever fixture at a major tournament.
Georgia boss Sagnol praises his side
"I don't want to say we are happy losers today but I think we can be proud of our performance," Sagnol told reporters.
"We have given such a nice image of the Georgian footballer but of course, we had a lot of opportunities to score, probably as much as Turkey did. But that's football.
"I'm sure in the future, in the next months and years, Georgia won't lose this kind of game. We are in a learning process, but we want to learn in a good way."
Turkey are the early leaders in Group F, with Portugal also on three points in second, having beaten Czech Republic 2-1 in their opening match of the tournament.
The top two teams in the section will lock horns next on Saturday evening, while Georgia will tackle Czech Republic earlier in the day, with both sides under pressure to pick up all three points after losses last time out.