The Team Sky leader looked to be in trouble more than once during the short but brutally tough penultimate stage but he was able to limit his losses to crest the final mountain in fifth place.
The Briton's nearest rival, Nairo Quintana (Movistar), attacked repeatedly on the iconic Alpine climb in a courageous effort to overcome his 2min 38sec deficit to the race leader.
While he was unable to maintain the pace of the Colombian climber, 2013 Tour champion Froome was able to settle into a rhythm on the wheel of team-mates Wout Poels and Richie Porte. In doing so, he not only retained the yellow jersey, but secured an advantage of 1min 12sec before the final stage to Paris.
Team Sky gave every last ounce of energy for the cause as the Movistar team looked to throw everything at the race leader on what was effectively the final day of competitive racing for the general classification.
Sky's Luke Rowe, Ian Stannard and Leopold König set an early tempo as the race departed Modane and as the peloton hit the climb of the Col de la Croix de Fer. Attacks soon came and Nicolas Roche and Porte dug deep to set a tempo as the race temporarily blew apart.
Froome shut the gap over the top of the climb, adding points to what would eventually prove to be a winning total in the king of the mountains competition as well.
Geraint Thomas, Poels, Porte and Roche all battled back on the descent to support Froome on the approach to the 13.8km fan-lined finale, keeping the pace high along the valley road.
Again Quintana attacked, finally pushing clear on Alpe d'Huez. His fourth acceleration saw him bridge to team-mate Alejandro Valverde, who was further up the road.
Despite being put under intense pressure Sky controlled the situation with Poels and Porte, who finished seventh and ninth over the line, setting a consistent tempo before Froome eventually pushed on to the finish.
Up ahead a race within a race played out as Thibaut Pinot (FDJ) held on to claim the stage win out of the breakaway, holding on by just 18 seconds over Quintana.
The huge day puts Froome on the verge of a second Tour title after his first success in 2013. This will be Sky’s third victory in the world's biggest bike race after Bradley Wiggins's win in 2012.
After the stage, Froome admitted that he had been pushed hard in the finale as he battled to hold on to the yellow jersey.
"It's unreal. I'm sure I haven't quite taken it all on board yet. It's an unbelievable feeling to be sitting here still wearing this jersey," said the 30 year old.
"There were so many things going through my mind going up that last climb. There were moments where I thought, 'Hold on a second I could be in danger here'. But then always having my team-mates with me, and having Wout and Richie there all the way until the end.
“I thought of all the sacrifices and the weeks of training camps. Time away from my wife and my family. Everything starts going through your head and I was on my limit there. I was hurting going up that last climb. But I just had to find something else just to keep pushing and get through today.
"It was only 110km but it felt like it was 300! It was such a hard stage!"
Sky Team Principal, Dave Brailsford heaped praise on Froome and the entire team but admitted that his riders had been worked hard on the final day in the Alps.
"It was a bit close in the end. After everything he has endured and put up with in the last few weeks Chris has shown real mettle and what it's all about," said Brailsford, referring not just to the physical duress of the race, but the fact that spectators had thrown unrine on, and spat at, the race leader from the side of the road.
“I don't think many people get to see what we see every day, and he's shown it in this race. He's a deserved winner and a credit to Britain."
"I think we knew what was coming. We had a bit of a bad day yesterday as a team. Wout saved the day really yesterday and he deserves a lot of credit for that."
Froome was isoloated on Stage 19 and lost another 30 seconds to Quintana who rode away from the race leader on La Toussuire.
“Today the lads were really geed up for it and they weren't going to make a mistake," Brailsford said. "They weren't going to throw that away and I thought they rode superbly. Richie Porte, whose been really ill for the last few days, he bounced back there today put a fantastic shift. All the lads they've been brilliant for three weeks. It's nice to win it.
"What I've known about Chris is that he is the most unbelievable competitor. He's the most polite, nice guy off the bike, but on the bike he is such a resilient character. I don't think I've ever met anyone like him. He's perfect for the job, but he deserves more credit than he gets. He's a true champion."