According to an update from the police department, an officer responded to screams for help in the parking lot of a Petco at 23710 Commercial Center Dr. at about noon on Wednesday.
The officer tried to stop the suspects' vehicle, leading to a short chase through the Reserves at Town Center neighborhood.
When the chase reached a dead-end street, two men, identified as Tyre Hartley and Hakeem Thomas, ran away into the area.
Rosenberg police officers, the Fort Bend County Sheriff's Office and the Richmond Police Department were able to find the suspects with the help of residents and took the men into custody.
Police say Hartley and Thomas were found with the victim's property.
Both of them may now be facing a number of criminal charges, including robbery, tampering with evidence and evading in a vehicle.
Officials say Hartley was out on a $60,000 bond for capital murder in Harris County.
Before the victim's purse was snatched in the Petco parking lot, she was at the bank. Investigators say she was followed from the bank to the store.
Rosenberg police said this was the second time in just a matter of weeks that officers responded to a crime like this and were able to recover a victim's items and arrest suspects.
"It's ridiculous to see a suspect out on bond for Capital Murder continuing to victimize the public. The Rosenberg Police Department is committed to keeping our community safe and will continue to be vigilant in our mission of public safety. We can only hope judiciary in our neighboring county does the same," said Rosenberg Police Chief Jonathan White.
Authorities noted that in both incidents, the suspects were from Houston/Harris County.