Orica-GreenEdge rider Chaves pipped Dutchman Tom Dumoulin of Giant-Alpecin to the line in the 158.
7-kilometre trek by one second, with Team Sky’s Nicolas Roche a further eight seconds back in third and Irish compatriot Daniel Martin of Cannondale-Garmin another five seconds behind in fourth.
Roche’s Sky team mate Chris Froome, the 2015 Tour de France winner who is bidding for a rare Tour-Vuelta double, was seventh, 30 seconds behind Chaves, who will wear the leader’s red jersey for Monday’s third stage into Malaga.
A fine win for the Colombian was overshadowed by the disqualification of Italian Nibali, the 2014 Tour de France champion who won the Vuelta in 2010.
Following a pileup with around 30 kilometres remaining, television footage showed Nibali hanging onto his Astana team car as he tried to catch up with the leaders and organisers had no choice but to expel him.
He eventually finished almost one and a half minutes behind Chaves.
“The film shows clearly that Nibali was clinging to the car for 200 metres,” said Bruno Valcic, the president of the race commissaires.
Astana director Alexandre Shefer, who was driving the car, is also out of the race, he said.
The opening stage of the 70th edition of the Vuelta on Saturday, a team time trial won by BMC Racing, did not count towards the general classification due to safety concerns about several narrow, sand-covered stretches in Marbella.
Chaves though seized his chance with real racing underway.
“We talked among ourselves and how to deal with everyone around us and the main thing to do was to attack these guys so that’s what we did,” Chaves told reporters.
“I felt like I was in a good position and in the end I did it and I got this (red) jersey.”
Froome, who also won the Tour de France in 2013, was runner-up in last year’s Vuelta behind Spaniard Alberto Contador.
Contador is not contesting his home race after winning the 2015 Giro d’Italia but struggling on the Tour.
Frenchmen Jacques Anquetil (1963) and Bernard Hinault (1978) are the only riders to have won the Tour and the Vuelta in the same year.
(Reporting by Iain Rogers, editing by Mark Meadows)