Maguire stroked the ball home to earn his side a vital away goal in the first round qualifying tie, ahead of next week's second leg at Turner's Cross.
Linfield debutant, Northern Ireland goalkeeper Roy Carroll, made a number of fine saves to deny Cork a second.
Paul Smyth headed over the bar from six yards in the first half for the hosts.
Beaten Irish Cup finalists Linfield, who were also runners-up in the Irish Premiership, were without injured defender Sean Ward, while Jimmy Callacher is on honeymoon.
Cork came into the tie in confident mood as they lie second in the Irish Premier Division, three points behind leaders Dundalk.
Visiting goalkeeper Mark McNulty tipped Ross Gaynor's free-kick over the bar in the 15th minute, then Maguire's shot across goal was well gathered by Carroll, who returned home from France as part of Michael O'Neill's Euro 2016 squad on Monday.
McNulty was called into action again before the break as he denied Kirk Millar, pushed away Karl Sheppard's defensive corner and made a fine stop from Andrew Waterworth.
Smyth squandered his chance when his headed effort went agonisingly over the bar and Carroll saved from Garry Buckley.
After Maguire broke the deadlock, the same player forced the busy Carroll into a point blank save and Stephen Lowry cleared Kenny Browne's goal-bound effort off the line.
The Blues keeper was then equal to Kevin O'Connor's 16-yard volley and the lively Maguire flashed a shot narrowly wide.
A 63rd-minute penalty from Sean Maguire saw Irish League club Linfield go down 1-0 to League of Ireland counterparts Cork City at Windsor Park on Thursday.