A header from Caitlin Hayes on 27 minutes settled the match at Partick Thistle’s Firhill Stadium, with the Spaniard tasting silverware for the first time since arriving in Scotland in January last year.
It is only the second time that Celtic have lifted the SWPL Cup, having done so back in 2010, while City’s wait to get their hands on the trophy goes on a little longer, having last won it in 2015.
Alonso, whose team defeated Rangers on the way to the final, said: “I'm absolutely delighted, it's a very magic day. I thought we controlled the game, had so many chances, but the most important thing is we got the win.
“We were fighting for every ball. I'm so proud of the girls. Silverware is amazing.
“We beat the best teams in the country to win the trophy.”
Matchwinner Hayes said: “Playing for this team and this club is an honour. It means the absolute world to every single player. I just cant put it into words.
“Under Fran Alonso we're an unstoppable force and we'll just keep going.”
Celtic were the better team for much on the final in front of a crowd of 3,645 – a record for such an event.
They had started the brightest and had good early chances through Charlie Wellings and Clarissa Larisey, but took the lead just before the half-hour mark when Hayes powered a Sarah Harkes free-kick beyond Lee Alexander.
City’s best chance of the first half came through Priscilla Chinchilla, but she could not finish at the back post.
Eileen Gleeson, the City manager, brought on Mairead Fulton at the break to try and get back into the match, but it was Celtic who came out flying and Alexander made a fine stop from Harkes – partner of Dundee United midfielder Ian – on 49 minutes. The Scotland internationalist then made another intervention to deny Jacynta Galabadaarachchi.
Celtic’s Chloe Craig had a goal disallowed for offside on the hour mark, with City’s best chance coming when Claire Walsh hit the bar with a header. However, they could not peg Celtic back as captain Kelly Clark lifted the trophy.