Everton twice led through goals from winger Richarlison, who arrived from Watford, the latter coming despite Phil Jagielka's reckless red card.
But Nuno Espirito Santo's men ensured they would avoid defeat in their first Premier League match since the 2011/2012 season when Jimenez — one of four new faces in the Wolves starting XI — nodded home Ruben Neves's cross.
Neves had earlier levelled proceedings with a classy free-kick straight after Jagielka's red, and Marco Silva will reflect on a frustrating debut outing as Everton boss.
A rocking Molineux was silenced in the 17th minute. Michael Keane attacked a Leighton Baines free-kick that Wolves failed to deal with and Richarlison prodded home from close range.
The pyrotechnics that preceded kick-off were not initially followed with fireworks by the hosts on the pitch, but the complexion of the match changed four minutes before the break when Jagielka lost control of a routine pass then inevitably saw red for an ugly lunge on Diogo Jota.
From the resulting free-kick Neves curled an unstoppable effort into the top-right corner.
Cenk Tosun and Jimenez exchanged missed efforts before Everton regained the initiative after 67 minutes.
Richarlison combined with Tosun on the left of the area and coolly stroked home into the far corner.
But Wolves fought back again and Jimenez earned a share of the spoils 10 minutes from time when he met Neves's excellent left-wing cross with a glancing header past Jordan Pickford.