Djokovic was thrashed by in-form sixth seed Verdasco in the semi-finals of the Monte Carlo Masters in their last meeting and the match looked like it might follow a similar plot early on.
The Serb was under constant pressure, slamming his racket down in frustration after being pushed around in a rally before caving in on serve in the seventh game.
Djokovic, the 2008 Rome champion, responded bravely though, breaking when Verdasco was serving for the set. The pair traded breaks again before the Spaniard took the set in the tiebreak.
Djokovic did not panic and read his opponent's meaty serve skilfully in the second set to break three times to one and claim it.
But Verdasco had a little more in the tank, even though he has played a lot of tennis recently after winning last week's Barcelona Open, and prevailed with an ace after three hours and 17 minutes of big-hitting action.
The Serb said he has been hindered by health problems recently but was confident he would be one of the main contenders for the French Open, which begins next month.
"I've had real problems with allergies for the past two months and this has been really troubling," he told a news conference.
"But everything else is in order and I'm happy with the way I played, so definitely the French Open is the place where I want to get a good result.
"I was very close to victory and I know that this match could have gone either way." Verdasco's reward was a semi-final against compatriot David Ferrer, who make light work of Frenchman Jo-Wilfried Tsonga, triumphing 6-4 6-1 after knocking out Britain's world number five Andy Murray on Thursday.
Holder Rafael Nadal, seeking his fifth Rome title in six years, faces Swiss Stanislas Wawrinka in his last-eight match later on Friday.
World number one Roger Federer, who lost his opening match in the singles on Tuesday, was knocked out of the doubles in the quarter-finals along with compatriot Yves Allegro by American pair John Isner and Sam Querrey, 6-4 6-4.
