The visitors appeared to have done enough to grab a point on the road after Siyanda Xulu had cancelled Sirino’s first-half goal, but Lakay rose from the bench to decide the contest late on.
Maritzburg, on the other hand, remain without a win, sitting second from bottom.
The action swung from one end to the other as Maritzburg seemed determined to upset their hosts who remain unbeaten in the league in five games.
It was Sundowns who however nearly went ahead 11 minutes into the encounter but Themba Zwane narrowly missed the target after being fed by Jose Ali Meza off a counter by goalkeeper Denis Onyango.
The Uganda captain was then called to repel Pumlani Ntshangase’s shot two minutes later as Maritzburg responded.
Scoring chances kept on coming for both sides with Sundowns forward Gaston Sirino blasting his effort over the cross bar while on the other end Mosa Lebusa almost beat his own goalkeeper Onyango when placed under pressure.
Maritzburg’s Ghanaian goalkeeper Richard Ofori was nearly punished by Meza when he failed to clear Daniel Morgan’s back pass but the Venezuelan's shot went just wide.
Sirino then produced a magical moment six minutes before half-time after being released by Sibusisio Vilakazi to beat Rushine De Ruck and leave him sprawling on the ground, before neatly curling the ball into the back of the net for Sundowns’ opener.
The visitors came back from the breather fired up and as they piled pressure on the Brazilians. They had a penalty call turned down when it appeared as if Thapelo Morena had handled the ball inside the box from a Daylon Claasen shot.
It did not take long for Maritzburg’s pressure to pay off 10 minutes into the second half with Xulu heading into the far post from a Morgan corner kick.
Xulu’s goal sparked relentless attacking by Sundowns that saw Morena being denied by the upright.
Ofori kept Maritzburg in the contest by denying Tebogo Langerman at close range off a chip from Hlompho Kekana on 68 minutes.
While it seemed Maritzburg had done enough to earn a point on the road, substitute Lyle Lakay fired in after a quality supply from Man-of-the-Match Sirino deep into injury time to claim three points for the Brazilians.