Spain are making their Olympic women's football debut at the Paris Games but are leading contenders to win gold after their World Cup triumph in Australia and New Zealand last year.
They fell behind against Japan in Group C in the western French city of Nantes to Aoba Fujino's superb early free-kick, but Bonmati soon equalised as she rounded the goalkeeper to score midway through the first half.
Spain then grabbed the winner in the 74th minute when Mariona Caldentey exchanged passes with Bonmati before firing in.
With 12 teams split into three groups of four, there is margin for error as the two best third-placed sides will advance to the quarter-finals.
That will provide some comfort for Japan, silver medallists at London 2012.
A strong Spain starting XI featured seven players who were in the line-up for last year's World Cup final win over England in Sydney, plus Alexia Putellas, the two-time former Ballon d'Or winner.
"We have started the Games very well. I'm happy for the win. (The World Cup loss against) Japan left us with a thorn in our side," Bonmati said.
"The goal we conceded didn't change our mentality. We played our football and we deserved the win."
In the same section, two-time silver medallists Brazil beat Nigeria 1-0 in Bordeaux.
Former world player of the year Marta, in her sixth Olympics at the age of 38, had an effort disallowed for offside before setting up Gabi Nunes for the only goal late in the first half.
Swanson at the double for USA
The USA have come to the Games with a young squad but with high hopes of success under new coach Emma Hayes.
They were comfortable winners against Zambia in Nice but should have triumphed by a greater margin after netting three times in the first half against opponents who had a player sent off before the break.
Trinity Rodman and Mallory Swanson both hit the woodwork before Rodman - daughter of former NBA superstar Dennis Rodman - scored on 17 minutes with a lovely turn and finish in the box.
Swanson made it 2-0 on 24 minutes when she controlled Lindsey Horan's pass and finished, and she netted again just a minute later, this time rounding the goalkeeper to slot in.
Zambia's Pauline Zulu was left in tears as she was sent off following a VAR review shortly before the break for a foul on Sophia Smith. However, the USA could not add any more goals with the extra player.
Also in Group B, 2016 gold medallists Germany outclassed Australia, winning 3-0 in Marseille with Marina Hegering and Lea Schueller both scoring headers before Jule Brand wrapped up the victory.
The USA and Germany meet each other in Marseille on Sunday.
France survived a wobble to beat Colombia 3-2 in Lyon, where there were plenty of empty seats to greet the host nation.
Marie-Antoinette Katoto scored twice in the first half either side of a Kenza Dali strike as France appeared to be cruising.
However, Catalina Usme pulled one back from a penalty early in the second half and substitute Manuela Pavi further reduced the deficit before a red card for Mayra Ramirez ended Colombian hopes of snatching a point.
Canada shrug off spying scandal
In the same Group A, reigning Olympic champions Canada shrugged off a spying scandal to claim a 2-1 win over New Zealand in Saint-Etienne.
Mackenzie Barry gave New Zealand the lead before a sparse crowd at the Stade Geoffroy-Guichard.
Arsenal's Cloe Lacasse levelled in first-half stoppage time for Canada, who beat Sweden on penalties in the final in Tokyo three years ago. Evelyne Viens then fired in the winner 11 minutes from time.
Canada's build-up had been overshadowed after an assistant coach and an analyst were sent home from the Olympics on the eve of the game.
The analyst, 43-year-old Joey Lombardi, was also given a suspended eight-month prison sentence for flying a drone over a New Zealand training session this week in Saint-Etienne.
Head coach Bev Priestman apologised and took no part in the game against New Zealand, feeling it would not be appropriate.
"As a Canadian, these are not our values. We are not cheats," said defender Vanessa Gilles, who described the episode as a "humiliation."
