Sainz finished less than a second off pole position and less than a tenth behind the Red Bull of Max Verstappen, who qualified fifth in the first non-Ferrari and non-Mercedes car.
“Congratulations to all the team, because we got both cars in Q3, which is something that hasn’t happened for a long time at this team,” said Sainz.
“It shows we are working well, we are going in the right direction.
“A tough winter and the second half of last year trying to understand the problems with last year’s car is now starting to pay off.
“We are learning, we are improving the car and today we are here, nearly as the best of the rest, which was unthinkable three or four months ago. We were half a second off this.”
Sainz, who retired from the season-opening Australian Grand Prix, admitted he was at a loss to explain why McLaren was so close to the cars in front after lapping just half a second slower than the Mercedes.