Leg-spinner Beer (3-14) took wickets in his opening over of two separate spells - getting rid of Jason Smith (18) just prior to tea, then removing Jason Mulder (seven) and Heinrich Klaasen (five) late in the final session.
Briggs, who trapped the dangerous Temba Bavuma lbw for 63, took one wicket, as did seamers George Garton Abidine Sakande to leave South Africa 'A' trailing Sussex by 307 runs, after they were bowled out for 458 just after lunch.
The day belonged to Briggs, though, after he managed to notch a maiden first-class century just prior to lunch.
Briggs, who had just one first-class half-century to his name before today, ended unbeaten on 120 as Sussex were bundled out for 458.
Rudi Second ( *) and Dane Piedt ( *) will resume for the Proteas 'A' side, with 157 still needed to avoid the follow-on.
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