Pulido, who plays for the Greek club, Olympiakos, cut his wrist when he punched a glass pane on a door as he tried to escape before police arrived.
Pulido, 25, was abducted at gunpoint on Saturday night in his home town of Ciudad Victoria in Tamaulipas state.
A 38-year-old man has been arrested.
Officials say the man had confessed to belonging to a local criminal gang. Police are searching for another three men believed to have been involved in the kidnapping.
State prosecutor Ismael Quintanilla said the masked gang had taken Pulido to a house in Ciudad Victoria where he eventually found himself alone with one of his abductors.
"They traded blows. He takes it [the phone] and calls [emergency number] 066. It all happened very quickly," Mr Quintanilla told Imagen radio.
An official report of the calls Pulido made to the emergency operator, obtained by the Associated Press, revealed that he threatened and beat the kidnapper while on the phone, demanding to be told where they were.
In one of the calls, Pulido said police were outside and starting to shoot so he described what he was wearing to avoid being mistaken for a kidnapper.
Pulido had been abducted when his car was surrounded by several vehicles as he was leaving a party with his girlfriend on Saturday night.
Masked men whisked him away, leaving his girlfriend unharmed.
Pulido's family received a phone call on Sunday demanding a ransom payment, Mr Quintanilla told reporters. No ransom was paid.
Pulido, with one of his hands bandaged, told reporters early on Monday: "[I am] very well, thank God."
Tamaulipas is one of Mexico's most violent states, and Mexico recently deployed more security forces to tackle cartels operating in the area.
The country has one of the world's highest kidnapping rates, with government figures saying some 1,000 people are abducted every year.
Pulido joined Olympiakos last July and finished the season with six goals in 15 games.
He was part of Mexico's squad at the 2014 World Cup in Brazil, but was not called up for the upcoming Copa America tournament.

Kevin Standing's vehicle was taken from his home in Patcham, East Sussex, on Saturday morning. It did not have a tracker and there was no CCTV evidence.
He said he had wrongly assumed an officer would visit him, but he was told there were no lines of inquiry.
Sussex Police said they focused on crimes that "cause most harm".
Mr Standing said he received a letter from the force on Tuesday saying the "investigation was closed" and to check the CCTV footage of local garages.
"It basically says to car thieves in Sussex, 'carry on stealing cars because there's very little chance you're going to get caught'," he said.
Ch Insp Bruce Mathews said proportionate inquiries had been completed.
"Our investigations teams focuses its efforts on the crimes which cause the most harm.
"Operating with new demands against a shrinking budget, we can't do everything but that doesn't mean we will be ruling out certain types of crime such as shoplifting or vehicle crime.
"We will continue to do so where there are lines of inquiry."
The force said a marker had been placed on the vehicle to bring it to the attention of Automatic Number Plate Recognition (ANPR) cameras.

Polling booths opened at 07:00 BST in the area's 15 constituencies, with results expected to be declared after midnight.
Votes will be counted after the polls close at 22:00 BST.
For the latest news from all the counts on Merseyside, go to our election live service or check the results on your constituency profile page.
International footballer Alan Pulido, who has been rescued after being abducted in Mexico, fought one of his kidnappers and used his phone to call police, officials have revealed.
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A motorist whose Â£40,000 Jaguar car was stolen from his driveway has said he is "astounded" after police said they would be closing the case.
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People are voting across Merseyside in the general and local council elections.