The only other time the Romanian fifth seed had strung together three successive victories at the All England Club, she made it all the way to the semi-finals in 2014.
She was also spared the torment of running on and off court on yet another showery day at this year's championships because her showdown with Bertens, originally scheduled on Court Two on Friday, ended up being contested under the Centre Court roof.
"I'm really excited that I'll play the fourth round, it's one of my special grand slams," said Halep, whose French Open challenge fizzled out five weeks ago after she was forced to play her fourth round match in misty rain.
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"It was amazing today, I played good tennis and I'm happy I could win in two sets. I felt every ball. I felt my legs. The court was very safe and I really liked that the court was indoors."
Bertens had all the credentials to create an upset following her run to the semi-finals of the French Open, which included a first-round win over Australian Open champion Angelique Kerber.
"This match was important for me. It was a big challenge. I knew she's in good form. She did a great job in French Open, so she had a lot of confidence before this match," added Halep, who lost to Bertens in their only previous Tour level clash.
When Bertens broke the world number five in the first game of the match, the alarm bells must have started ringing for Halep as she stood at the baseline with her head hanging.
However, the Romanian quickly snapped back into focus to break back in the next game and twice more to bag the set with a crosscourt service return winner.
The 24-year-old jumped into a 3-0 lead in the second set and booked a last-16 date with either Alize Cornet or American ninth seed Madison Keys when Bertens whipped a forehand wide on match point.
Her trouble free progress through the first week of the grasscourt major would have been particularly satisfying for Halep as she had to forgo playing in any Wimbledon warm-up tournaments due to an Achilles injury.
"For three days I had unbelievable pain in my Achilles and I couldn't walk. I could not play at Birmingham, so I came here straight to practice," said the 2014 French Open runner-up, who has yet to drop a set at this year's tournament.
"I can say I am okay and I am fit now.
"At times I don't know what is going on with my Achilles but I was 100 percent for today's match and I hope for the next round it will be the same."
(Reporting by Pritha Sarkar, editing by Martyn Herman)
