Djokovic made his return to the court in Austria having not played since Roland Garros and has now spent 293 weeks as the world's best player, edging closer to Roger Federer's record of 310.
By winning the final, Rublev improved to 39-7 for the season, matching Djokovic's number of wins. No other player won more than 28.
The fifth-seeded Rublev led 6-4, 4-1 when Anderson quit the match with a right thigh issue.
Vienna Open 2020: Novak Djokovic suffers heavy loss to Lorenzo Sonego but insists securing top spot is priority
Having won two rounds in the Austrian capital, 33-year-old Djokovic is virtually guaranteed equalling Pete Sampras's record of securing the year-ending top ranking for the sixth time.
Fognini, 33, had a first-round bye and was set to open in the second round against Spain's Roberto Carballes Baena in the tournament played on clay on the Italian island of Sardinia.
Australian Open 2020: Rather than losing mind, Nick Kyrgios keeps head down to get the better of Gilles Simon
Nick Kyrgios won the opening round against Lorenzo Sonego and survived an emotional lapse late in the third set to beat Simon 6-2, 6-4, 4-6, 7-5 in two hours and 49 minutes at the Australian Open.
Australian Open 2020: Nick Kyrgios says he's playing for 'a lot more than myself' after winning first-round match
Kyrgios put on a vintage show for a packed Melbourne Arena on Tuesday with a 6-2, 7-6(3), 7-6(1) victory over Lorenzo Sonego in the first round of the Australian Open
French Open 2019: Roger Federer says winning title might not be 'in his racquet' on return to Roland Garros after four years
Federer will make his Roland Garros return on Sunday with a first-round tie against unheralded Italian Lorenzo Sonego
An erratic Novak Djokovic suffered a surprise 6-3, 4-6, 6-2 defeat against Daniil Medvedev in the Monte Carlo Masters quarter-finals.
Monte Carlo Masters: Novak Djokovic, Rafael Nadal breeze into quarter-finals; Daniil Medvedev bests Stefanos Tsitsipas
Novak Djokovic turned in a steady performance with a dozen winners and unforced errors, while his opponent committed nearly 30 unforced errors in 68 minutes
Monte Carlo 2019: Novak Djokovic beats Philipp Kohlschreiber in scrappy contest; Guido Pella knocks out Marin Cilic
Djokovic was able to avoid a second straight loss to Kohlschreiber after the 35-year-old beat him last month in the Indian Wells third round
Miami Open: Novak Djokovic cruises past Bernard Tomic; Naomi Osaka, Serena Williams advance to the next round
Novak Djokovic put his Indian Wells disappointment behind him on Friday at the ATP and WTA Miami Open with a ruthless 7-6 (7/2) 6-2 destruction of Australian Bernard Tomic to move into the third round.