It's been a slow start to the season for Ferrari, which has not adapted as quickly as runaway leaders Mercedes to the new fuel-efficient six-cylinder engines introduced to the sport this year.
At the Bahrain GP two weeks ago, Alonso and teammate Kimi Raikkonen could manage no better than ninth- and 10th-place finishes, respectively. Days later, the team parted ways with principal Stefano Domenicali after six years.
But Ferrari has made improvements on the car since then, giving at least Alonso a boost in Shanghai under the watch of new team principal Marco Mattiacci.
"We felt more competitive and now in the race being here on the podium is some kind of surprise for us, a nice surprise, finally," he said. "We didn't have the start of the season that we would like but at the end of the day, we're still in the fight."
Alonso, who was the defending Chinese GP champion, said he's reaching the same comfort level in the car that he had in 2012 when he finished just three points behind Red Bull driver Sebastian Vettel in the drivers' championship.
He managed to keep pace with the Mercedes cars in practice on Friday, and though he didn't get close to passing winner Lewis Hamilton in Sunday's race, he stayed close to second-place Nico Rosberg until the end.
"In Bahrain, we were one minute behind the leaders, ninth and 10th, and today we are on the podium, seven seconds behind Nico," he said. "Hopefully I can keep going like this. I felt more comfortable with the car and we will not give up."
Alonso may have fared better in Shanghai, but his teammate Raikkonen continued to struggle. The Finn failed to make it into the top 10 in qualifying, starting 11th on the grid, and only moved up three spots to eighth by the finish.
"Hopefully we found some reason or at least some cure for it, to fix it, whatever it is. In the race, (the car) just was slow," he said. "Obviously there's a lot of work to do. We haven't had any single race that we've been happy with the team the whole time."