Bester's scrambled 79th minute strike - which benefited from a goalkeeping blunder by Moeneeb Josephs - followed a brace by teammate Bongi Ntuli, while Kwando Mngonyama and Sibusiso Vilakazi netted for the Students at Bidvest Stadium.
Nineteen-year-old Mngonyama gave the home side the lead in the seventh minute. Arrows had conceded a free kick out on the right flank after a foul by left-back Mzivukile Tom, with Mngonyama heading home Matthew Pattison’s floated delivery.
Arrows were shell-shocked by the early goal and tried by all means to construct meaningful build ups, but their efforts were proving fruitless until the 27th minute when they finally found the equaliser.
Wits lost the ball through Pattison in midfield and were hit by a ferocious counter attack by Abafana Bes’thende. Their defence was split open as they tried to play an off-side trap but it failed as Bester slipped the ball through for an unmarked Ntuli to tap home.
Four minutes from the break Arrows nearly took the lead when Ntuli fed Bester, but the Namibian missed an open net as he headed wide with his former Orlando Pirates teammate Josephs off his line.
After that failed attempt Arrows found themselves behind in less than 60 seconds. Ayanda Lubelo found his skipper Vilakazi with a slick low cross and the 24-year-old midfielder tapped in simply to make it 2-1.
But 15 minutes into the second half, Manqoba Mngqithi’s men made it 2-2. Ntuli was the man who scored as he connected with a ball from the left flank and blasted Josephs’s net from close range.
Bester then snatched the spoils late on, as his mis-hit volley somehow crept through the clutches of Josephs.