Djokovic, twice a winner in Cincinnati, dominated the baseline rallies in his 6-3 6-2 win over Monfils and extended his perfect record against the Frenchman to 19-0 - the most lopsided unbeaten ATP head-to-head record in the Open Era.
The Serbian made the most of a loose service game from Monfils and broke to love at 5-3 in the first set to close it out.
After racing to a 5-0 lead in the second he faltered on his first attempt to serve it out, but completed the win two games later in an hour and eight minutes. Djokovic will next face home favourite Taylor Fritz.
"We've been playing each other in different parts of the world, also in juniors," Djokovic said. "Early on, I struggled with him physically.
"We haven't played for quite a few years. It's great to see him back playing at a high level."
World number one Alcaraz had not looked like himself in an uneven third-round performance on Tuesday but was firing on all cylinders on Thursday as he harnessed his mighty forehand to chip away at Paul's defences in the rain-interrupted battle.
Paul cracked the code to beat the 20-year-old earlier this month in Toronto but a handful more errors from the 14th seed this time around helped Alcaraz get the upper hand in his 7-6(6) 6-7(0) 6-3 victory.
"It was a really tough match," Alcaraz said. "Really, really happy with the level and think I'm getting better and better."
Alcaraz came back from a break down four times in the first two sets but squandered three match points in the second.
The Spaniard was serving at 4-3 and up a break in the decider when rain stopped play for over an hour. He broke Paul's serve again in the final game of the match to book a quarter-final clash with Australian Max Purcell.
Alexander Zverev upset third seed Medvedev 6-4 5-7 6-4 in a clash between former champions, breaking the Russian three times and saving six of eight break points.
The German 16th seed came into the match with a 6-9 record against Medvedev and having lost all three of their meetings this year. He will next face France's Adrian Mannarino.
"Very difficult conditions but also a very difficult opponent," Zverev said of Medvedev.
"He is somebody that gives you absolutely nothing. You have to win the match yourself and that's what I did today and I am pleased with that."
Poland's unseeded Hubert Hurkacz unleashed 11 aces and 27 winners to cruise past Tsitsipas 6-3 6-4 in a brisk one hour and five minutes, setting up a meeting with Australian lucky loser Alexei Popyrin.
