Zverev is targeting a second Rome title at the Foro Italico next week. He captured his first Masters there in 2017 before also winning in Montreal later that year.
Rafael Nadal lost to Alexander Zverev 6-4, 6-4 after comfortable wins against up-and-comers Carlos Alcaraz and Alexei Popyrin.
Djokovic is closing in on a ninth championship in Australia, which would add to his own record for a man. And an 18th Grand Slam title overall, two fewer than rivals Roger Federer and Rafael Nadal.
Five men's singles players to watch at the Australian Open Grand Slam tennis tournament, which starts on Monday after a three-week delay over the coronavirus.
Alexander Zverev bounced back after a tough singles defeat to Novak Djokovic to send Germany into the ATP Cup semis.
Alexander Zverev rallied from a set down to beat dangerous Denis Shapovalov and open his season with a fighting victory in the ATP Cup.
Alexander Zverev insisted he is on track to contend for a maiden Grand Slam title despite a mounting personal toll off the court.
The 21-year-old German, ranked fourth in the world, is part of the highly-touted "NextGen" crop of 20-somethings who are making an impact on the ATP Tour.
Zverev joined a list of back-to-back Washington champions that includes Americans Andre Agassi and Michael Chang and Argentina's Juan Martin del Potro.
Alexander Zverev, playing for the third day in succession, was shocked by Ernests Gulbis, ranked 138, in a gruelling five sets.
Alexander Zverev had just lost the third set when bad light forced play to be suspended late on Thursday evening.
Rafael Nadal is 100 points ahead of Roger Federer going into the grasscourt season where the Swiss will be looking to close the gap.
Rafael Nadal insisted Sunday that his stunning 6-1, 1-6, 6-3 comeback win over Alexander Zverev which delivered an eighth Rome Masters title will have no impact on his French Open campaign.
German second seed Zverev was 3-1 up in the decider before two rain stoppages halted his momentum.
For rising German star Alexander Zverev it was a tenth consecutive win after back-to-back title runs at Munich and Madrid.