Gift Motupa's early goal was cancelled out by Peter Shalulile before Mokete Mogaila sealed the points for Owen Da Gama's charges with a second-half strike.
And they showed a great sense of urgency in the opening stages of the encounter with Motupa opening the scoring in the 13th minute.
The former Orlando Pirates man used his head well to send the ball past Marlon Heugh, who took over from Tapuwa Kapini in goal.
However, their excitement was shortlived as the home side leveled matters five minutes later through Shalulile.
The Highlands Park man positioned himself well to nod a cross past Darren Keet.
The combination of Simon Murray and Motupa was just too hot to handle for Highlands Park, but the home side still managed to hold on and keep the Students at bay before the break.
Murray performed way below par in the second half, and he forced Gavin Hunt's hand to replace him with Haashim Domingo with the hour-mark fast approaching.
At this stage, Hunt surely realized that he needed a goal to at least move further away from Sundowns, who are three points behind with three games in hand.
Leaving Lehlohonolo Majoro on the bench proved too costly as Wits failed to break the Highlands Park defence and were left frustrated for the better part of the half.
The Lions of the North then hit back with 20 minutes to go through Mogaila, who rounded Keet before slotting the ball into an empty net.
Majoro was finally introduced in the final 15 minutes of the game, but it was too little too late as Highlands Park held on to blow the title race wide open.
The win also saw Highlands Park continue their push for a top-eight finish, and this result will go a long way in ensuring that they achieve this objective.
Ea Lla Koto conceded a penalty in the 28th minute, and Rhulani Manzini stepped up to give the Chilli Boys a lead.
Free State Stars tried to launch a comeback, but their strikers failed to put the ball into the back of the net as the Chippa defence held on firmly to protect their goalkeeper.
On 84 minutes, Kurt Leintjies sealed Chippa's win with a sublime finish to put the game beyond Ea Lla Koto's reach.