Tshegofatso Mabasa broke the deadlock in first half added time and Namibian Deon Hotto put the result beyond doubt by scoring after 78 minutes in a packed 25,000-seat Gaborone stadium.
Jwaneng had caused one of the biggest shocks in Champions League qualifying by eliminating Pirates from the last edition of the premier African club competition after a penalty shootout.
Pirates were later criticised for resting several first choices for the first leg, which they lost 1-0, and the Buccaneers did not repeat that mistake, fielding a full strength side.
The return match is on Saturday in Soweto and it would be a shock if Pirates do not win again and cruise into the group stage, where the minimum prize money is $800,000 (€720,000).
Mamelodi Sundowns, semi-finalists in the last two editions, brushed aside Mbabane Swallows of Eswatini 4-0 with Brazilian Lucas Ribeiro claiming two goals before being substituted.
Musa Lebusa and new signing Iqraam Rayners were the other scorers for the Pretoria outfit, who played the away leg at one of their two grounds in the South African administrative capital.
Swallows ceded home advantage because Eswatini does not have an international-standard stadium.
Five-time champions TP Mazembe from the Democratic Republic of Congo were too good for Red Arrows of Zambia, winning 2-0 on the road in Ndola.
Oscar Tshikomb ended the stalemate on 66 minutes and Merceil Ngimbi scored six minutes later to give the Congolese a huge advantage before hosting the return match in Lubumbashi on Saturday.
Young Africans of Tanzania, a club who could go even further than last season when they fell to Sundowns in the quarter-finals, won 1-0 away to Commercial Bank of Ethiopia in Addis Ababa.
Zimbabwean Prince Dube scored on 45 minutes for Yanga, whose Argentine coach Miguel Gamondi had expressed concern about tiredness with many players on Africa Cup of Nations duty this week.
Al Merrikh, forced to host Moroccan visitors FAR Rabat in South Sudan because of the civil war in Sudan, surrendered a two-goal lead in a thrilling 2-2 draw.
Samani el Sawi and Mohamed al Qabbani, with his third goal of the campaign, gave Merrikh a two-goal lead they squandered as Mohamed Hrimat and Abdelfettah Hadraf scored for FAR.
© Agence France-Presse
Photo: Alche Greeff/Gallo Images