Toro Rosso currently are in the proverbial driver's seat, with 53 points, with Renault on 49, and Haas-Ferrari on 47.
Toro Rosso also hold the tie-breaker, meaning Renault need to out-score them by five points to claim the lucrative sixth spot.
Six points are up for grabs for seventh spot in the Abu Dhabi Grand Prix, four for eighth, two for ninth, and one for tenth.
Mercedes' Lewis Hamilton secured the drivers' title - his fourth - at the Mexican Grand Prix last month.
Hartley, who debuted at the US Grand Prix a week earlier, has impressed with his performances since replacing French rookie Gasly in Austin and has secured a full-time drive for 2018.
Toro Rosso have earned just one point in their last five events, but a good drive by Hartley, or teammate Pierre Gasly, can clinch them their best finish since 2008 - and the substantial financial reward.