Deadlocked at half-time, Chiefs wasted little time in the second stanza as Mathoho nodded home a Siphiwe Tshabalala free-kick, before Nkhatha doubled the advantage midway through the half.
The win was enough to send the Soweto giants three points clear of second-placed Mamelodi Sundowns, who visit FNB Stadium on Saturday, in what could prove to be the title-decider.
A quiet opening 15 minutes saw little in the way of goalmouth action, save for Bernard Parker’s 15th minute volley from dead in front, which somehow struck teammate Nkhatha on the way and stayed out, much to the frustration of the home supporters.
Chiefs applied plenty of pressure as the half wore on, with little success, as Arrows did well to soak up wave after wave of attack.
The home side won several set-pieces in dangerous areas but failed to make them count, as Parker and Tefu Mashamaite came close, but were unsuccessful.
Chiefs enjoyed the lion’s share of possession and dominated the play in their opponents’ half, but poor finishing let the defending champions down late in the first half, as Siboniso Gaxa blasted wide from a promising position deep in Arrows’ territory.
Level at the break, the pair traded blows early in the second period as Arrows’ Manti Maholo and half-time replacement George Lebese flashed wide inside five minutes.
Chiefs, however, were rewarded for their persistence seven minutes after the break as Mathoho glanced home from Tshabalala’s well-taken free-kick from the left, rising above the Arrows’ defence and heading the hosts into the lead.
The Durban side struggled to get going after the interval and had precious few attempts on goal, Bonginkosi Ntuli’s drilled effort in the 66th minute a highlight, despite only finding the side-netting.
The Glamour Boys found their rhythm and looked likely to extend their lead as the clock wound down, and they did exactly that with 20 minutes left to play as Nkhatha rounded-off a superb team goal by the Soweto giants.
The Zimbabwean international did well to work himself into a dangerous position as Tsepo Masilela laid off a neat ball to the striker, who squeezed a left-foot shot past Bartman from a difficult angle, sending the home side to their feet as the ball trickled over the line and in for Chiefs’ second.
Chiefs never looked in doubt and saw out a morale-boosting victory, which will come as a welcome respite following their disappointing exit from the Caf Champions League last weekend.