Ebou Adams volleyed the Rams into an early lead, but Vakoun Bayo replied with an outrageous scissor-kick on the half-hour mark.
Sissoko had the last word, scoring on the rebound in the 76th minute to make it three Championship wins out of three for the club he rejoined in the summer.
Watford have also won an EFL Cup tie; only twice before in their history as a league club have they begun with four straight wins.
Sissoko, 35, has been impressive in midfield, having spent two seasons at Nantes after his first Watford spell ended in 2022.
"He is pivotal to what we are trying to do," said Cleverley, who is in his first full campaign as Watford manager.
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