In an extremely tight Q3 field, Alonso's 1m29.542s yielded him sixth on Saturday's grid.
And while he was a tantalisingly close 0.005s off Sergio Perez in fifth and just half a tenth of George Russell in third, Alonso was buoyed by the result because he had doubts about his AMR24's one-lap speed.
"It was a nice surprise to find ourselves competitive," Alonso grinned. "After winter testing we had some doubts in terms of one-lap pace.
"In free practice, it was a different car this weekend, we felt more competitive. But normally we run maybe more engine [power] or less fuel or whatever and we find [the] reality sometimes in qualifying, so we were very cautious into qualifying about our possibilities.
"We found ourselves quite competitive in Q1, in Q2 and then in Q3. Now we are in the mix. Within one tenth we are together with Ferrari, in front of Hamilton, together with the McLarens. So it's a massive surprise and extremely happy."
Meanwhile, team-mate Lance Stroll qualified 12th after missing out on a Q3 slot by less than a tenth.
When Alonso was asked by Autosport where he thought his surprising pace came from, he said his new machine reacted very well to any set-up changes Aston Martin applied to cope with Bahrain's tricky Sakhir circuit.
"I think the car was more connected," the two-time F1 world champion replied. "We had some difficulties last week in winter to really feel the needs of the car. It was quite inconsistent.
"This weekend, all the set-up changes we are trying are doing exactly what we expect from them and this is always a nice thing when you're trying to fine-tune a Formula 1 car to extract the maximum.
"So, the extra level of confidence in the car was the positive thing about this weekend."
Similar to his doubts about Aston Martin's qualifying pace, Alonso also remained cautious about its race performance after some more lacklustre long runs, which projected his team to be further behind Ferrari and Mercedes over a stint.
"We had some so-so runs in winter testing and yesterday we didn't look particularly good," the Spaniard explained.
"It's going to be an extremely tight race. Racing in a group of cars is never an easy thing to manage in terms of tyres and things like that, so let's see how we deal with those problems.
"It's a very, very good start. A little bit unexpected, but we take it. If we want to compete with Ferrari and Mercedes and these teams, we need to raise the level of development throughout the season.
"Last year we started with a good base car, but we got stuck there for many races. This year, we changed the concept of how to design the car and the upgrades.
"So, to start out strong, it brings me a lot of optimism for the future."
