Palpatine didn't use the Force, but Anakin most certainly did.
Hatches and drag fins
They were well within the atmosphere now, and still moving far too
fast. Anakin opened all the hatches and extended every drag fin that
still worked, trading the growing heat from the increased friction for
a decrease in speed. - RotS: Junior Novel
Steering thrusters
Anakin spared a glance for the Chancellor, who was clinging grimly to
his seat. He’s an administrator; he’s not used to this. But he didn’t
have time to explain things to the Chancellor, not if they were going
to survive this. “I’m going to shift a few degrees and see if I can
slow us down,” Anakin told Obi-Wan. “We’re heating up,” Obi-Wan
warned, and began calling out numbers.
I know, I know. Anakin played the controls, opening and closing
hatches, using steering thrusters to brake, anything to slow their
fall. - RotS: Junior Novel
Shields
“Keep us level,” he told the droid, and went back to work to slow them
down. “Steady,” Obi-Wan said. “Five thousand.”
“Hang on,” Anakin said. “This may get a little rough. We lost our heat
shields.” - RotS: Junior Novel
The Force
And at the same time, he [Anakin] draws power from the Force. He gathers
perception, and luck, and sucks into himself the instinctive,
preconscious what-will-happen-in-the-next-ten-seconds intuition that
has always been the core of his talent. And then he begins.
On the downbeat, atmospheric drag fins deploy; as he tweaks their
angles and cycles them in and out to slow the ship’s descent without
burning them off altogether, their contrabass roar takes on a
punctuated rhythm like a heart that skips an occasional beat. The
forward attitude thrusters, damaged in the ship-to-ship battle, now
fire in random directions, but he can feel where they’re raking him
and he strokes them in sequence, making their song the theme of his
impromptu concerto.
And the true inspiration, the sparkling grace note of genius that
brings his masterpiece to life, is the soprano counterpoint: a
syncopated sequence of exterior hatches in the outer hull sliding open
and closed and open again, subtly altering the aerodynamics of the
ship to give it just exactly the amount of sideslip or lift or yaw to
bring the huge half cruiser into the approach cone of a pinpoint
target an eighth of the planet away.
It is the Force that makes this possible, and more than the Force. Anakin has no interest in serene acceptance of what the Force will
bring. Not here. Not now. Not with the lives of Palpatine and Obi-Wan
at stake. It’s just the opposite: he seizes upon the Force with a
stark refusal to fail.
RotS: Official Novelisation
"He then declares that they're coming in too hot. (Too fast)"
I think the "too hot" in this case could be taken both literally and figuratively... – reirab Mar 7 '16 at 1:38