Gran Canaria ended up shooting just 11 of 31 (34.5%) inside the arc and four of 25 (16%) from long range.
Jolly dominated Gran Canaria in another important department as well, the rebounding.
The hosts hauled in 40 to just 27 for the visitors.
Neda Lokas had 19 points and five rebounds for the winners, who will look to finish off their opponents in the second leg in Spain next week.
Tina Thompson and Linda Frohlich appeared in a European game for Municipal Targoviste for the first time.
The Christmas holiday signings are two of the biggest names in the sport and each played well in their new club's 90-68 first-leg win at Ruzomberok.
Thompson had 13 points and 14 rebounds while Frohlich 15 points and five boards.
It was Shay Doron, a EuroLeague Women All-Star, who had the biggest game with 29 points for the winners.
Lizanne Murphy scored 16 points in defeat.
Lattes Montpellier grabbed the upper hand in their tie with Spartak Noginsk.
The French team claimed a 67-61 triumph on the road.
Pauline Krawczyk, a member of France's EuroBasket Women gold-medal winning side last year, poured in 19 points for Montpellier.
BC Dnipro edged a 59-57 thriller in Ukraine against Spanish outfit Ibiza Sport Island.
Iuliia Iakhina's two free-throws at the end gave the home side victory in the first leg.
USO Mondeville romped to an 84-68 triumph at Baschet ICIM in Romania.
Lenae Williams led all scorers with 28 points for the victors.
Epiphanny Prince had 20 points and eight rebounds for Botas Spor in their 74-50 rout CCC Polkowice.