The National South clash, played in awful conditions, looked set to end 0-0 but Alexander turned one point into three with his tenth goal of the season.
It left Adam Murray’s team third in the table, still just three points behind leaders Weston.
See pictures by Lydia and Nick Redman on this page and the ones linked and get all the Borough reaction in the Herald, out every Friday morning.
1. Eastbourne Borough v Bath City pictures by Lydia and Nick Redman (27).jpg
Eastbourne Borough v Bath City, National League South Photo: Lydia Redman : Lydia and Nick Redman
2. Eastbourne Borough v Bath City pictures by Lydia and Nick Redman (24).jpg
Eastbourne Borough v Bath City, National League South Photo: Lydia Redman : Lydia and Nick Redman
3. Eastbourne Borough v Bath City pictures by Lydia and Nick Redman (25).jpg
Eastbourne Borough v Bath City, National League South Photo: Lydia Redman : Lydia and Nick Redman
4. Eastbourne Borough v Bath City pictures by Lydia and Nick Redman (28).jpg
Eastbourne Borough v Bath City, National League South Photo: Lydia Redman : Lydia and Nick Redman