The China PR-based striker took advantage of sloppy defending to tap in a long Davies Nkausu throw in front of a capacity 40,000 crowd at Levy Mwanawasa stadium.
Katongo was a constant threat to Uganda, netting again in the opening half only to have his effort disallowed before being foiled by the woodwork after the break.
Midfielder Rainford Kalaba was another Zambian to impress and came close with a first-half free-kick that beat goalkeeper Denis Onyango only to fly into the side-netting.
Uganda, seeking a place at the Africa Cup of Nations for the first time since finishing runners-up to hosts Ghana in 1978, spent most of the match on the back foot and were lucky to finish only one goal behind.
The return match is scheduled for mid-October and the winners qualify for the 16-nation tournament to be staged by South Africa in Johannesburg, Durban, Port Elizabeth, Nelspruit and Rustenburg.