Havertz converted from the penalty spot at the second attempt to earn Chelsea a 2-0 second-leg victory and knock out Borussia Dortmund 2-1 on aggregate.
The German forward, who has struggled to establish himself in a consistent role under Graham Potter this season, also impressed with his general play.
The 23-year-old also played a part in Raheem Sterling’s opening goal as Chelsea struck twice in quick succession either side of the half-time interval.
While Havertz has scored only seven times in all competitions during this campaign, Henry sees similiarities between his game and that of Van Persie, particularly with regards to the German’s hold up play.
“I thought he was good on the first goal,” Henry said on CBS Sports. “You could see he held the ball ever so well.
“It reminds [me] sometimes a little, very little, of a Robin - the way he can hold the ball. Robin van Persie was very good with his left foot. The touch was always immaculate to drive, to bring people along.
“This is why I think out of the guys that used to be wingers or a No 10, he plays as a No 9 because back to goal, he can hold the ball well.
“Now he needs to make sure he can transform that into more goals, because you can play off him.”
Havertz’s goal from 12 yards came after he was permitted to re-take an initial effort that struck the post.
A VAR review found that Dortmund players had encroached into the box before Havertz had taken his penalty.
It proved a crucial intervention, with the German’s eventual conversion taking his side in to the last eight and giving a significant boost to Graham Potter.
The Chelsea manager had been under significant pressure with the club toiling in tenth in the Premier League table.
They next travel to face Leicester in the league on Saturday afternoon.