The pair had travelled from their home near Madrid and were present as Contador roared with delight when he crossed the finish line then made his trademark 'pistol shot' salute as he received the leader's jersey.
Contador's victory, following a surprise attack 55 kilometres from the line, was his first since his doping suspension for the banned substance clenbuterol ended on August 5, and put him on track to claim a second Vuelta victory on Sunday in Madrid and his fifth Grand Tour.
"He deserves this win," Fran, who is also Contador's agent, told Spanish television. "He has really suffered (during the suspension). Thank God, he's back.
"He managed to surprise them all and he did it brilliantly."
Contador's mother said simply: "It's his day."
Before Wednesday's attack, Contador had been lying 28 seconds behind overnight leader Joaquim Rodriguez, but he now leads by one minute 52 seconds over fellow Spaniard Alejandro Valverde.
Contador said of the attack: "I had an angel on one shoulder, saying: 'Don't do this, they're going to roll you over' and a devil on the other saying: 'Go for it'.
"On this occasion, I didn't listen to the angel.
"People said to me: 'Where are you going so far from the line and in fact it felt a bit like a kamikaze attack."
Contador described his victory as "one of my three most important triumphs of my career, together with the one I took when I came back from my operation (for brain surgery in late 2004), in the Tour Down Under (in January 2005) and my win in Paris-Nice in 2007."
Contador said he wanted to dedicate the victory to "all the people who have supported me (during the ban), all my friends.
"This has been a very important day for me, because at this point very few people thought I could really win this race. I hadn't been able to drop Rodriguez on the climbs, but here I could. This is a very big step forward."