The Qataris had taken a 37th-minute lead through Adil Boulbina, but quickfire goals from Nunez and Hernandez sealed the points for Simone Ingazhi's side.
Al Hilal dominated the opening exchanges, but it was Al-Duhail who took the lead.
Boulbina latched onto Youssouf Sabaly's searching pass from deep inside his own half to outpace the retreating Joao Cancelo, rounding goalkeeper Yassine Bounou to score from a tight angle with a composed finish.
The home side thought they had levelled in stoppage time when Turkish defender Yusuf Akicicek lashed a fierce shot into the bottom corner, only for the effort to be ruled out for an infringement in the build-up.
Half-time substitute Nunez did level, the former Liverpool forward finishing a move that also featured Sergej Milinkovic-Savic and resulted in Malcom cutting the ball back for the Uruguayan to bobble his shot past Salah Zakaria.
Hernandez put Al Hilal in front when he punished a poor defensive header, thumping his volley from the edge of the area into the Kingdom Arena turf before the ball zipped beyond Zakaria.
Al Hilal moved alongside fellow Saudis and defending champions Al-Ahli, plus Emirati pair Sharjah and Al Wahda, on three points in the western league standings after the opening round of matches.
The competition is using the Swiss league format to determine the eight qualifiers for the next phase, which will be played in March, from the 12-team opening round.
Earlier, Iran's Tractor FC held on to draw 1-1 with hosts Shabab Al-Ahli in Dubai despite playing much of the second half with 10 men.
Tomislav Strkalj put Tractor in front with a blistering strike from outside the penalty area that gave goalkeeper Hamad Al-Meqbaali little chance.
Domagoj Drozdek's straight red card for a lunge on Shabab Al-Ahli's Saeid Ezatolahi left the Iranians short-handed from the 51st minute, and 14 minutes later the home side levelled through Guilherme Bala after a quickly taken free kick.