Altidore scored his first goal in 2014 for club or country just after the half-hour mark, tapping in Fabian Johnson's cross, while he added a second after half-time to ensure the USA completed their FIFA World Cup preparations with three wins from as many games.
By contrast, Nigeria will head to Brazil having failed to win any of their pre-tournament friendlies with the loss at EverBank Field following draws with Scotland and Greece.
Victor Moses earned a penalty in the 86th minute, and converted for a consolation goal for Nigeria.
During the USA's pre-World Cup training camp, the American media had regularly questioned coach Jurgen Klinsmann's insistence on playing Altidore at the point of his formation, with the 24-year-old having failed to score in six internationals.
Altidore had also been poor for Sunderland last season, scoring just two goals in 39 appearances in all competitions.
But the powerful striker was clinical against Nigeria on Saturday, scoring both goals as the USA celebrated goalkeeper Tim Howard's 100th cap in style.
Both coaches made changes for their final pre-World Cup friendly with Klinsmann choosing to play all three of Michael Bradley, Kyle Beckerman and Jermaine Jones in midfield for just the second time in his tenure.
The USA had been quite open in midfield during their 2-1 win over Turkey on June 1 and Klinsmann appeared focused on shutting down space against Nigeria.
Beckerman and Alejandro Bedoya came into midfield with Graham Zusi and Brad Davis dropping to the bench, while DaMarcus Beasley replaced Timothy Chandler at left-back.
For Nigeria, coach Stephen Keshi promoted Joseph Yobo, Juwon Oshaniwa, Ramon Azeez and Shola Ameobi, who replaced Elderson Echiejile, Kenneth Omeruo, Ahmed Musa and Emmanuel Emenike from the starting line-up against Greece on Tuesday.
Echiejile has been ruled out of the World Cup with an injury.
Nigeria started better and were keen to get the ball quickly to their forwards out wide in an attempt to get in behind the USA's defence.
In the seventh minute, a clever pass from Moses played in Ameobi but he could only stab his shot into the side netting.
The same duo also combined nine minutes later, with Moses' corner finding Ameobi and his header bounced up and had to be tipped away by Howard as the ball looped towards the top corner.
But as the half wore on, Klinsmann's midfield wall of Bradley, Beckerman and Jones began to get on top with Nigeria struggling to break down the USA's disciplined defensive shape.
With Beckermann and Jones providing the defensive cover, Bradley was free to sniff out interceptions and look to create when the home side gained possession.
The 26-year-old Toronto FC midfielder got on the end of a fine attacking move at the midway point of the first half, forcing Nigeria goalkeeper Vincent Enyeama into a low save down to his right, which sparked a period of dominance for Klinsmann's men.
From the resultant corner, Bedoya curled a shot just beyond the top corner of Enyeama's goal and, soon after, another set piece saw Dempsey's acrobatic volley fly over the bar.
In the 32nd minute, the USA achieved a deserved breakthrough with Jones receiving the ball on right side of midfield and playing the ball outside to Bedoya, who picked out Johnson in the box and the Hoffenheim full-back squared a pass for Altidore to tap into the net.
Nigeria's best chances in the first half came from corners and in the 44th minute, Howard had to make a save at the near post, although the ball almost squirmed between his legs.
The visitors had more possession in the first half and continued that trend after half-time, although they were unable to penetrate the USA's defence.
Just after the hour mark, the USA reminded Keshi's men of the threat they posed on the counter-attack with Bradley feeding Dempsey and the hosts' skipper stepped inside one opponent only to fire his shot straight at Enyeama.
In the 64th minute, Bradley picked out Altidore in the box with a fine lofted pass and the Sunderland striker powered his way past Yobo before thrashing the ball into the net.
Having already defeated Azerbaijan and Turkey in the lead-up to the World Cup, Klinsmann and the Americans will arrive in Brazil with a record of four wins, a draw and a loss this year.
They will begin their World Cup finals campaign against Ghana on June 16, while Nigeria will play Iran on the same day.
