Burrows missed an open goal in the first half but made up for that by scoring with a late header.
On Boxing Day, Loughgall secured their second trophy of the season by beating Mid-Ulster rivals Coagh United 2-1 in the Bob Radcliffe Cup final.
Alan Murphy opened the scoring for Loughgall and Dean Smith doubled their lead before Scott McCordick pulled one back for Coagh after half-time.
Portstewart beat Tobermore United 2-1 in the Craig Memorial Cup final.
Gavin Doherty put Tobermore ahead but goals from Andrez Kleczkawski and Lee Rushe ensured Portstewart's victory.
Abbey Villa play Comber Rec in the Border Cup final at Wilgar Park on Thursday (1300 GMT).