Karim Bellarabi put the hosts in front shortly before half-time and when Kevin Volland doubled the lead after the break, Leverkusen looked to be heading for a comfortable victory.
Gomez had other ideas, however, glancing home Jakub Blaszczykowski's right-wing cross after 79 minutes to spark a stunning conclusion at the BayArena.
The striker headed Maximilian Arnold's corner in two minutes later and Gomez completed his 12th Bundesliga hat-trick from the spot after the influential Blaszczykowski was brought down to turn the game around for the visitors.
But Leverkusen claimed a point in the 89th minute, Bellarabi setting up 17-year-old Kai Havertz for a powerful low finish that confirmed the teenager as the youngest Bundesliga goalscorer in his club's history.
Gomez has now scored 15 goals in the nine games Jonker has coached him, the pair having previously worked together at Bayern Munich, but Wolfsburg are only a point above the relegation zone following the six-goal thriller, while Leverkusen are two places higher in 11th.