Cavin Johnson started his tenure as Kaizer Chiefs interim coach on a difficult note after the Soweto giants were edged 2-1 by Golden Arrows in a Premier Soccer League match at Mpumalanga Stadium on Saturday.
Mutizwa grabbed a brace, first scoring in the 20th minute before completing his double nine minutes into the second half.
It was another difficult outing for Amakhosi who recorded a three-game losing streak across all competitions.
The Soweto giants remain eighth on the PSL table as Arrows keep on flying and returned to second spot after spending Friday night in third position.
With Johnson having taken over from Molefi Ntseki on Monday, there were high expectations of him to help change Amakhosi's fortunes.
But the situation remained the same for the Glamour Boys whose chances of catching up with log leaders Mamelodi Sundowns are getting slimmer.
Chiefs goalkeeper Brandon Petersen, central midfielder Edson Castillo, Mduduzi Shabalala and defender Hlanti were back to start in what highlighted a new era at Amakhosi.
Arrows unsettled Chiefs who were still trying to find their way into the contest when Mtizwa broke the deadlock.
But Amakhosi responded shortly after with Hlanti beating Arrows goalkeeper Ismail Watenga.
It looked like the contest was headed for a stalemate as they did not look content with being a goal apiece.
But after the breather, Mtizwa then connected from Nduduzo Sibiya's cross to reclaim the lead for Abafana Bes'thende.
Just after Mtizwa scored his second goal, Velemseni Ndwandwe forced Petersen to make a desperate save with a low shot.
Chiefs tried to come back into the match and Castillo shot just over the bar as conditions became unfavourable with rain.