The Clever Boys were awarded a penalty after just 13 minutes after Lunga was adjudged to have handled in the box, which allowed Simon Murray to step up and slot home from 12-yards out for his fourth league goal of the season.
Arrows goalkeeper Maximillan Mbeava was called into action moments later as he showed good reflexes to keep out Gift Motupa's glancing header.
Motupa was not to be denied on 26 minutes as the former Orlando Pirates man headed home a cross from Deon Hotto to double Wits' lead.
Gavin Hunt's men looked to add a third goal just over 10 minutes later, but Motupa saw his powerful effort palmed away by Mbaeva.
That proved to be the final opening in a lively opening 45 minutes, although Arrows hardly made any forays into the Wits 18-yard area.
Arrows came out firing in the second half and reduced the deficit as a result, with Seth Parusnath finishing off a well-worked counter attack.
The comeback was complete on the hour mark when Wayde Jooste converted from the penalty spot to set up an exiting final 30 minutes.
With Wits throwing a two-goal lead, Gavin Hunt threw on Majoro and later Gabadinho Mhango as they went in search of a winning goal.
Nduduzo Sibiya had a chance to put Arrows ahead in the closing stages, but he was unable fire past Keet in a one-on-one situation.
In the end, 2-2 was how the score remained as Hunt's troops will rue missed chance close in on league leaders Orlando Pirates.