World number 12 Fognini slumped to a 7-6 (7/5), 7-5 defeat by the 150th-ranked Pospisil at the Caja Magica.
The Spaniard draws level with rivals Djokovic and Roger Federer, who have also finished the year in top spot five times, and moves one behind six-time end-of-year number one Pete Sampras.
The 21-year-old Greek is the fourth first-time champion in as many years at the season finale, which has proved a poor predictor of future success.
The Greek 21-year-old is the youngest champion since Lleyton Hewitt in 2001 and the fourth first-time champion at the season-ending event in as many years.
Djokovic lost to Roger Federer on Thursday, missing out on a place in the ATP Finals semifinals in London, revealing afterwards that he had been suffering pain in his elbow.
The Czech world number 103 won 13 titles, reaching a career-high of fourth in the rankings in 2015.
The Greek sixth seed, 17 years younger than his 38-year-old opponent, beat the Swiss at the Australian Open but had fallen to him twice since then.
Tsitsipas, who topped the group, will play six-time champion Roger Federer in Saturday's semifinals while Zverev will meet Dominic Thiem.
In the final, Nawaf defeated compatriot Meshari Nayef.
Tsitsipas, 21, had already qualified for the semi-finals before Friday's match after beating Medvedev and Zverev.
The tournament is being held at the Khalifa International Tennis and Squash Complex.
The Swiss will face the Group Andre Agassi winner on Saturday.
The defending champion was asked about the incident during the post-match press conference following his 6-3, 6-2 defeat on Wednesday.
Bob Bryan said the duo had opted to end their 2019 season after the US Open in order to remain fresh for next year.
The straightforward victory took Tsitsipas's head-to-head record against Zverev to 4-1.