The win means Sundowns are just a point from a place in the last four - with two games remaining.
They only reached the group phase after the disqualification of DR Congo's Vita Club, for using an ineligible player.
In Saturday's matches in the other group, Zesco United beat ASEC Mimosas and Al Ahly and Wydad Casablanca drew.
Sundowns' victory came thanks to goals from Tiyani Mabunda and Khama Billiat.
They lead their group with six points from two games so far - ahead of Zamalek with three, and Nigeria's Enyimba - who have yet to register a point.
There are only three teams in their pool, after the elimination of Entente Setif of Algeria following crowd trouble.
On Saturday, in the other group, Zesco United of Zambia boosted their hopes of progressing with a 3-1 victory over ASEC Mimosas of Ivory Coast, as Egyptian giants Al Ahly saw their own challenge falter.
Zesco moved up above ASEC to second in Group A, a point behind leaders Wydad Casablanca who drew 0-0 at bottom side Al Ahly.
Only the group winners and runners-up qualify for the semi-finals, which leaves Al Ahly with little hope of advancing.
Al Ahly coach Martin Jol now faces a huge challenge following the result at home to Wydad Casablanca from Morocco which brought his side their first point.
Ahly were desperate for maximum points after a disastrous start to the mini-league phase which has seen them slump to the foot of their group.
Pre-season favourites for a record-extending ninth title, the Cairo Red Devils had already fallen to a 3-2 away defeat to Zesco United and a 2-1 loss at home to ASEC Mimosas.
The 0-0 draw in Alexandria strengthens Wydad's position at the top of Group A, with John Toshack's men on course to qualify for the last four.
History is stacked against Ahly securing a top-two finish and a semi-finals place in a competition offering a $1.5m first prize and a ticket to the 2016 Fifa Club World Cup.
Only one of 120 clubs - USM Alger of Algeria in 2003 - have reached the semi-finals after losing their first and second mini-league matches.
Earlier on Saturday, Zesco United faced a formidable ASEC Mimosas team who had excelled in away matches this year, winning three out of four before the clash in Ndola.
But the hosts, who have now won five Caf matches at home this season, dominated the Ivorians from the start, going into the break 2-0 up thanks to goals from Jackson Mwanza and John Ching'andu.
ASEC did fight back in the second half, halving the deficit through Youssouf Dao in the 75th minute, but it took just three minutes for Zesco United to make the game safe.
An impressive piece of individual skill from Idriss Mbombo in the penalty box gave Zesco a 3-1 victory,
South Africa's Mamelodi Sundowns beat Egypt's Zamalek 2-1 in Cairo on Sunday to close in on a place in the semi-finals of the African Champions League.