The Argentine levelled for Barcelona 15 minutes from time at Stamford Bridge, after a wayward pass from Andreas Christensen was pounced on by Andres Iniesta.
Willian's fine strike just after the hour mark had put Chelsea in command after earlier hitting both posts in the first half.
He fine-tuned his radar after the interval, however, rifling home into Ter Stegen's bottom-left corner to give Chelsea the lead.
Had man-of-the-match Willian scored rather than hitting the post twice in the first half, the London club might have been home and hosed by the time the Brazil global did find the back of the net after the break.
Valverde has said that he feels "very positive" about the game, but appeared keen to ensure that the La Liga outfit do not get complacent with Chelsea being forced to chase a result in the reverse fixture.
"We were very close to playing a flawless game and I think we paid dearly for one mistake", he said, according to Marca.
Messi, along with Suarez, were kept at arm's length for much of this game, but it only takes one slip against this Barcelona team, even when they are out of sorts.
Besiktas, making their debut in the knock-out stages of the Champions League, face a near impossible task in the return leg in Istanbul on March 14 if they are to prolong their European adventure.
"I hope that to see this type of performance for a long time", said Conte of a player who has not always been first-choice this season.
"It will not be easy, we must be realistic because we are talking about Barcelona".
Fantastic anticipation from Iniesta allowed him to take the ball in his stride and immediately find Lionel Messi who made no mistake in finding the net.
Playing Hazard and Morata would have risked the entire game plan with Chelsea then falling a man short in midfield against that of Barcelona which has dismantled teams in Spain this season. They pressed us very high and made life hard for us. We have to go there and play the same game. "I saw at 1-0 the possibility of us to try and exploit the situation in the best way to score a second".