However, there were ugly scenes at full-time as angry Super Eagles fans peppered Ghana's players and staff with water bottles thrown from the stands as they left the pitch.
Arsenal midfielder Thomas Partey gave the Black Stars a shock lead against the run of play in the 10th minute, before Watford defender William Trost-Ekong levelled from the penalty spot 12 minutes later after Ademola Lookman was fouled.
Ghana coach Otto Addo's game management was spot on as his team kept a defensive shape to earn a fourth appearance at the global showpiece.
Partey's early strike and goalkeeper Francis Uzoho's error helped Ghana advance to the finals on the away goals rule after the first leg finished goalless on Friday.
The Black Stars had missed out on Russia 2018, and their qualification denied Nigeria a fourth successive outing at the World Cup finals.
After conceding a penalty for the Super Eagles' equaliser, Ghana defended for much of the 90 minutes and rarely threatened the hosts.
Nigeria thought they had scored a second when Victor Osimhen went past Jojo Wollacott and slotted home, but the video assistant referee correctly ruled he was offside in the build-up to the goal.
Joe Aribo, Emmanuel Dennis and Lookman were all presented with opportunities but failed to punish Ghana. Leicester City's Daniel Amartey provided solid cover for the Black Stars' defence as they stayed disciplined at the back.
Dennis headed wide for the home side in the second half and Osimhen sent two acrobatic attempts past the post, but it was largely comfortable for Ghana in the closing stages as they held on to reach Qatar.
Piers Edwards of BBC Sport Africa provides an analysis at MKO National Stadium in Abuja.
Nigerian fans erupted in rage and uncontrolled frustration as the Super Eagles' World Cup exit was overshadowed by violence.
Locals pelted Ghana fans, numbering in the hundreds, and Black Stars players with water bottles, causing the latter to hide and shield their heads as they fought their way down the tunnel after a mass pitch invasion.
Local security permitted the nasty events, which included police striking supporters with batons, to continue for about five minutes, and were only momentarily interrupted when tear gas was deployed on the pitch.
A dugout had been overturned and smashed up by that point, as the unwelcome but all-too-familiar side of football violence reared its ugly head.
Ghanaian fans leaving the stadium expressed their amazement and displeasure with their treatment, while Fifa, the world governing body of football, will take a dim view of situations that require further explanation from both Nigerian security and football officials.
