Beattie had initially struggled to find his shooting boots - drawing a blank in his first six appearances for Swansea - but his 50th minute strike against Albion made it two in two games for the former Celtic marksman.
Beattie made no mistake with a clinical piece of finishing as he raced on to a pass from Mark Gower and beat Scott Carson with a low angled drive.
The win extended Swansea's unbeaten run to seven games - conceding just two goals in the process - as Albion's inconsistent form continued.
They have now picked up just four points from the last 15 and drew a blank in front of goal for only the second time in the Championship this season.
They were dominant in terms of possession in the first-half but it was Swansea who should have taken a lead into the interval.
Albion struggled to break down a resolute Swansea defence with Alan Tate's last ditch challenge denying Luke Moore and then Chris Wood squandering a golden chance when he spooned Gonzalo Jara's cross over the bar.
Swansea grew in confidence as the half progressed and created two clear cut openings only to be frustrated by Carson and some poor finishing.
First Carson denied Nathan Dyer with a point blank save from Gower's 38th minute corner.
Cedric Van Der Gun then gave Albion a major let off when he cut into the area five minutes before the interval only to slice his shot wide from 12 yards with just Carson to beat.
But Beattie was not about to let off Albion for a third time.
Predictably, Albion made a late push for an equaliser but the closest they came was when substitute Cox slid his 76th minute shot inches wide.
Ultimately, they were lucky not to slip to a heavier defeat as Carson pushed Thomas Butler's goalbound drive on to the post five minutes from time.