Jones was visibly delighted after coming through her second qualifying match in a demanding two hours and 17 minutes.
After Hontama ran away with the opening set, the players exchanged six consecutive breaks of serve at the start of the second before Jones took charge.
A run of four consecutive games ensured she would take the match the distance, but the tension only increased as the decider began with another five breaks of serve.
Crucially, as in the second set, Jones was first to dig in on serve, providing a springboard to victory as she eventually seized her third match point.
The Briton roared with delight before turning to embrace her supporters in the crowd.
Also through to the final round of qualifying in the men’s event is former US Open champion Marin Cilic.
The 36-year-old Croat, a French Open semi-finalist in 2022, beat Spain’s Pol Martin Tiffon 6-4 6-3 to set up a meeting with South African Lloyd Harris.
