Sauber's head of trackside engineering, Tom McCullough, had suggested after the Italian GP that Gutierrez was on the brink of outqualifying lead driver Nico Hulkenberg, which the Mexican achieved for the first time in Singapore.
McCullough believes Gutierrez's performance had been on the cards for several races.
"He has been very close to doing it many times but ultimately it hasn't quite happened," McCullough told AUTOSPORT.
"Here, he put it together when it really mattered, did what he needed to and delivered.
"The overall approach through the race weekend has been good, building up through the sessions.
"You only have to be quick in the important laps in Q2 and Q1. It's about understanding the right way of working, which he is learning a lot from Nico, who learned a lot from Rubens [Barrichello, at Williams] in his first season in the same way."
McCullough also believes the performance will be vital for Gutierrez's confidence.
Gutierrez has been knocked out in Q1 eight times so far this season and previously had failed to start a grand prix higher than 14th.
"When the car isn't that competitive, it's easy with a little bit less experience to be the one knocked out in Q1," said McCullough.
"It's not good for the driver confidence but today he has done what we all know he's very capable of doing.
"It's nice to put it together and it will give him some good confidence to go forwards."
Gutierrez talked about the need to take a more aggressive approach to qualifying strategy in the build-up to the weekend.
He believes this change in approach is key to his success in Singapore.
"To have a more aggressive strategy, first of all," said Gutierrez when asked what the key to his qualifying performance was.
"We made some mistakes in practice but it was the only way to find the edge of performance and to know where the edge is in extracting the most from the tyres.
"It's a great feeling to know we have found a solution to that."
McCullough is hopeful Gutierrez can carry his form over into the race, in which it is hoped both cars will fight for points.
"Part one is done," said McCullough. "Generally, Esteban has raced very well for us, his [tyre] management is good, he's a bright lad and doesn't do silly things.
"Now the next step is to race from a better position with the big boys."
Gutierrez did not set a lap time in Q3 because he did not have any fresh super-soft rubber left, meaning he was unable to try and repeat his seventh place in Q2.