The burglary took place at about 5.30am at a house on Altringham Road which is near the park.
An Avon & Somerset spokesman said: “Upon arrival, officers located a man and a woman with serious injuries. They were both taken to the Bristol Royal Infirmary where they remain in a serious but stable condition.
“Following inquiries, we have made four arrests in connection with this incident. Four men remain in police custody at this time.”
Any witnesses or anyone with information that may help the investigation is urged to contact the Bristol East Central team on the non-emergency number 101 or to contact Crimestoppers anonymously on 0800 555 111 or www.crimestoppers-uk.org