"It's going to be hard for someone to take more than five minutes in 125 kilometers (78 miles)," Froome said. "But having said that I don't want to be complacent and want to stay switched on until at least tomorrow evening."
Realistically, only an improbable slump make that impossible, given how he's been riding so far will stop the 28-year old from matching countryman Bradley Wiggins's success last year.
"I am excited, but quietly excited," Froome said. "It is a day where the whole team's going to have to stay alert and control that last stage. One final big effort, then we can start relaxing on the ride into Paris."
Costa secured his second stage win of the race, and third of his career, after catching Frenchman Pierre Roland about a quarter of the way up the final major ascent of Col de la Croix Fry.
German veteran Andreas Kloeden was second and Belgian Jan Bakelants was third.
The 204.5-kilometers (127-mile) trek featured two HC climbs and two Category 1 ascents between Bourg-d'Oisans and Le Grand-Bornand in the snow-capped peaks of the Alps.
Contador was tipped to attack Froome on the downhill stretch, but perhaps because of the rainy conditions, he held back.
"Even though there wasn't much attacking, it was really tough out there," Froome said. "For us the objective was to stay on the wheel (of the other contenders)," Froome said. "The team did a huge amount of work today. There are still 125 kilometers to go tomorrow."
Saturday's 20th stage from Annecy to Annecy-Semnoz features a Category 1 climb and finishes with an HC or Hors Categorie climb, meaning they are considered so tough they are beyond classification.
But Contador will need a miracle to claw back his deficit and may not even go for it.
"It all depends on how my legs are tomorrow," Contador said. "It depends how I feel."
Froome was not attacked up the first of the two big HC climbs to Col du Glandon.
Canadian Ryder Hesjedal and Spaniard Jon Izaguirre opened up a sizeable lead over the yellow jersey group once they went over the top.
As Hesjedal and Izaguirre reached the second HC of Col de Madeleine, the peloton was 10 minutes behind. Hesjedal forged ahead but was then overtaken by Frenchman Pierre Rolland.
The stage undulated through the valleys and up several big hills, including the Category 1 climbs of Col de l'Epine and Col de la Croix Fry, and then flew down to the ski resort of Le Grand Bornand in southeastern France.
Rolland maintained his lead up l'Epine zooming up the 7.3 kilometers (4.5 miles) in just under 19 minutes but Costa proved too strong for him. Costa also won up to Super-Besse ski station in 2011.
With the rain becoming heavier, Costa prepared for a long and slippery descent of some 13 kilometers (8 miles).
Contador chose not to take Froome on down it and risk jeopardizing his podium position. Colombian climber Nairo Quintana is only 21 second behind in third place.
"I didn't want to attack in the downhill," Contador said. "A lot of people like me and when they see me attacking downhill they get scared."
Froome sat on Contador's wheel whenever he could, forcing him to work and spend energy, and the Spaniard could not shake him off.
"There was a moment when I wanted to attack and thought about it," Contador said, "but then I thought it was best to reach the finish line."
