Q:

How did Chang'e-4 hover, rotate, and then descend so gracefully? (Video)

In this incredible video we can see Chang'e-4 in it's final approach and landing on the moon from the point of view of the spacecraft.
The view is horizontal as the spacecraft seems to stop and hover over the chosen site, and then the view pitches forward until it is looking straight down. Then the spacecraft descends and lands. Specifically 00:50 to 01:10 in the video.
The speeds are slow and the altitudes are low so I assume that the engine should be pointed mostly down the whole time, but that conflicts with the view.
Can someone explain to me how the spacecraft hovers so nicely and yet appears to pitch forward by 90 degrees so gracefully?

A:

The view is horizontal as the spacecraft seems to stop and hover over the chosen site, and then the view pitches forward until it is looking straight down.

According to the graph linked by @AlexanderVandenberghe, that pitchover is happening at 6-8km altitude, so I think what you're interpreting as a "stop and hover" is not a hover. It's falling, but the moon's surface is far enough away that you can't easily see the fall rate. Once it's more or less nulled the horizontal velocity, it pitches to vertical and begins to seek out its final landing site.
It's especially hard to judge the altitude and vertical speed throughout most of this video because the terrain is uniformly fractal -- it looks basically the same at a wide range of scales. 6km altitude and coming down at 100 m/s looks much the same as 600m coming down at 10 m/s.

