Romanian seventh seed Halep wrapped up a 6-1 6-3 victory over the Ukrainian eighth seed in one hour 13 minutes.
“It is one of the best moments of my life,” said Halep, whose previous best finish at Wimbledon was reaching the 2014 semi-finals.
Speaking to the BBC, the 27-year-old added: “I’m really excited but also nervous. I’m just trying to enjoy it as much as possible.
“It was not as easy as the score shows. I fought really hard, [Svitolina] is an amazing player and it’s always tough to play against her.”
On what has changed since 2014, she said: “I have more experience, I am positive on court and I am not giving up anymore. I have learnt many things in five years.”
Halep capitalises on gripping start
Halep and Svitolina, 24, had not met at a Grand Slam since the 2017 French Open but if the first game of their maiden grass meeting was anything to go by, it was going to be a lengthy affair.
Lasting almost 10 minutes, it featured two 23-shot rallies before Svitolina – who had held three break points – conceded the game off her backhand.
Halep converted her third break point to go 2-0 up with the following two games also going against the server.
At 4-1 down, Svitolina lost her serve once more as Halep – who hit 16 winners but also 12 unforced errors in the opener – went on to serve out the set with a forehand down the line on her sixth set point.
If she hadn’t already, Halep demonstrated her desire to win in the second set, holding her first three service games to love before going a break up at 4-3.
And she was to finish on a break too, sealing match point on the second time of asking after Svitolina slammed a backhand into the net.