The reigning double BSB champion qualified in eighth position for his fifth World Superbike event and worked his way up to sixth place, after a bad start, in race one.
Kiyonari was only ninth after the opening lap of race two, but this time worked his way aggressively forward to take fifth by lap five and third by lap 11 of 18, despite having never raced at the famous Italian track before.
The Japanese then battled leaders
Noriyuki Haga and Max Neukirchner for the remaining laps, taking the lead into the Ascari chicane for the final time - with only the fast Parabolica curve separating Kiyo from a shock debut win.
Kiyonari resisted both Haga and race one winner Neukirchner on the brakes, but Haga cut inside at the apex, forcing Kiyonari to correct his line, costing him the lead and also second position – as Neukirchner swept into second on the dash to the line.
"I am very happy with my results, but looking back at the race, I think I missed some chances. I made some mistakes and it stopped me from taking my first win," said Kiyonari, after standing on a WSBK podium for the very first time.
"I still struggled with my start in both races, but in race two my pace was good and a lot more consistent then the first one and I was able to catch up with the top group.
'"I was very excited to find myself riding up front. When I overtook Neukirchner and saw Haga in front of me, I thought, will it be possible to overtake him. When I did, I made a mistake and ran wide in the exit of the last corner. Haga tried to keep the inside and I went outside and had to close the gas," he explained.
"I want to thank my mechanics and my sponsors and hope that I can win the next race for them."
Kiyonari's team-mate
Carlos Checa finished eighth in race one, but crashed out of race two. Third Ten Kate rider,
Kenan Sofuoglu, withdrew the event on Friday after his brother was killed racing in Turkey.