Bo'ness moved up to second in the Super League
Centre-back Stuart Hunter got the only goal during the first half, his left-foot volley from a Robert Sloan cross ensuring the BUs took a grip on second place.
Greig McDonald missed a headed chance to secure the points in the second half, and home midfielder Derek Ure saw red after picking up two yellow cards.
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Hide AdNewtongrange Star made it ten goals in just two games with a 4-1 victory away to Broxburn Athletic, despite falling behind in the second half.
They rallied to leapfrog the Albyn Park men into fifth place with two of their four goals coming from the penalty spot.
Tonight, South Division champions Tranent Juniors host Super League champions-elect Bonnyrigg Rose at Foresters Park in the quarter-finals of the Fife and Lothians Cup (kick-off 7pm).
Defender Dean Hoskins is missing through suspension for the visitors, with Rose boss Robbie Horn set to freshen up his starting XI after Saturday’s 3-2 defeat of Hill of Beath.
Midfielder Lewis Hawkins it out injured for the hosts, who are bidding to extend their season by securing a spot in the semi-finals.