Hall had two goals and Nugent-Hopkins scored the other for the Oilers, who improved to 4-2-0 in exhibition games.
Ray Whitney and Shane Doan scored for the Coyotes, who have lost three straight and are 2-3-0 in the preseason.
The game was scoreless until there was just two minutes remaining in the first period when two players expected to be cornerstones for Edmonton combined on a power-play goal.
Playing on the same line for the second time, Hall, the 2010 first overall pick, drove hard to the net on the man advantage and took enough of Phoenix goalie Mike Smith's attention that Nugent-Hopkins, the 2011 first overall pick, was able to sweep in the rebound for his fourth preseason point.
The Oilers' future line, which included another first-round pick in Jordan Eberle, struck again just over a minute into the second period as Nugent-Hopkins made a long pass just above the top of the crease to Hall, who snapped home his second exhibition goal.
The third Oilers goal was more of the same as Nugent-Hopkins made a backhand pass from the slot to a hard-charging Hall, who sent a shot past Smith to the glove side.
Phoenix scored its first goal with two minutes left in the second on a penalty-killing gaffe by the Oilers, who allowed Whitney to receive a pass alone in front of the net and he swung around Nikolai Khabibulin and put the puck into the net.
Phoenix closed within a goal with five minutes remaining on another power play as Doan had a quick release on a feed from Patrick O'Sullivan for his second of the preseason.
Khabibulin finished with 18 saves for the win, while Smith stopped 29 shots.
Copyright by STATS LLC and The Associated Press
Arena: Rexall Place Location: Edmonton, Alberta
Attendance: 16,218 (96.3% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Ryan Nugent-Hopkins (1)
(Power Play) Assists: Taylor Hall, Jeff Petry
Taylor Hall (2)
Assists: Ryan Nugent-Hopkins, Tom Gilbert
Taylor Hall (3)
Assists: Ryan Nugent-Hopkins, Jordan Eberle
Ray Whitney (1)
(Power Play) Assists: Daymond Langkow, Patrick O'Sullivan
Shane Doan (2)
(Power Play) Assists: Patrick O'Sullivan, Daymond Langkow