Some 121 patients called at the hospital on 4 and 5 January - up 46 on the previous year.
The spike coincided with a flu outbreak which forced the closure of ward 12.
General Manager for Diagnostics, Nicole Hamlet, said the hospital had continued to provide "high quality care" at the "most challenging part" of the year.
She said dealing with illness over winter months brought "additional challenges" such as ward closures.
"We have robust planning measures in place to respond to this peak in activity," she said.
"Contingency measures have been in place over recent weeks to cope with the anticipated extra demand on the service, particularly over the festive break.
"We had planned to keep our non-urgent elective operations to a minimum at this busy time."
She said that despite admission pressures they had been able to "maintain patient flow throughout the service".
Ms Hamlet said that was due in "great part" to the "dedication and commitment" of staff across the NHS and their partners.
"Their dedication, support and ability to work under pressure have proved invaluable," she said.
NHS chiefs have praised staff who helped to cope with a 60% surge in emergency admissions to Dumfries Infirmary at the start of the new year.