Former Wolves star Neves slotted in from the penalty spot in the 74th minute, as Al Hilal completed a rapid comeback.
Having fallen behind to Lucas Zelarayan's 57th-minute opener, Al Hilal responded swiftly through Micheal before Salem Al Najdi fouled Mohammed Al Qahtani in the penalty area.
Ex-Barcelona winger Cristian Trello and Al Fateh coach Slaven Bilic were booked for their complaints, with Neves making no mistake, paving the way for Ali Al Bulayhi to seal victory in the 15th minute of an extended period of stoppage time.
Data Debrief
Al Hilal have now won 21 games on the spin in the league. They have scored 86 goals across their 28 matches this season, winning 26 in total.
They had 19 shots on Friday, accumulating 2.34 xG to Al Fateh's 0.25, with pass-master Neves creating three chances to go along with his goal.
In a game short of clear-cut chances, the hosts got a stroke of luck to help them beat Edouard Mendy.
The teams struggled to get going in the first half, with both goalkeepers only having to make a couple of comfortable saves apiece.
Riyad Mahrez had the best chance, racing in behind Al-Fateh's defence only to drag his low shot wide of the far post. However, his blushes were spared by the offside flag.
Djaniny broke the deadlock from range in the 54th minute – his scuffed shot took a wicked deflection off Ibanez, and Mendy could not keep it out despite getting hands to it after being wrongfooted.
Al-Ahli pushed for an equaliser, with Sumayhan Al Nabit cutting inside in stoppage time, but his low drive was straight at Peter Szappanos.
Data Debrief: Milestone win for hosts
While it was not a classic by any stretch, Al-Fateh will remember it as their 150th win in the Saudi Pro League (85 home, 65 away). They are the sixth club to hit that milestone in the competition's history.
Al-Fateh have now won five of their last 22 Saudi Pro League matches against Jeddah clubs (drawn six, lost 11), with all of those victories coming against Al-Ahli.
The Portugal captain, who moved to Saudi Arabia on a free transfer after his Manchester United contract was cancelled by mutual consent, opened his account with a late penalty at Prince Abdullah bin Jalawi Sports City Stadium.
Saudi Pro League leaders Al Nassr twice came from behind to secure a point on the road.
Ronaldo got up and running in his third game for his new club to deny sixth-placed Al Fateh.
The 37-year-old forward calmly dispatched his spot-kick in the 92nd minute before his team-mate Talisca, who scored Al Nassr's first goal to cancel out Cristian Tello's opener, was sent off in a dramatic finale.
Ronaldo had scored twice for Riyadh All-Stars in a 5-4 friendly draw against a Paris Saint-Germain side that included Lionel Messi and Kylian Mbappe last month.
