Mr Baba, also a former Deputy Director General of the Ghana Prisons Service, polled 351 votes to beat four other challengers.
The former Ghana Handball Association President had contested the primaries three orevious times but lost to John Akologo Tia.
Second in Sunday’s primary came Awunnore Edward with 265 votes with Charles Bazimwomit placing third with 53 votes.
James Atore and Rockson Atitiba came fourth and fifth respectively with a total of 8 votes.
The NDC had won the Talensi seat since the return to multi-party democracy but only lost it to the New Patriotic Party (NPP) in 2012.
But Robert Doaneng Nachinab Mosore after just three years in office abdicated the seat to occupy the paramountcy of Tongo traditional area.
Meanwhile the NPP also elected Thomas Doanab, an accountant and lawyer with the Nsawam Government Hospital, as its candidate for the by-election.
Mr Doanab, 51, beat competition from two others to win the slot. He polled 182 votes out of a total of 399 to win his party’s primary, held on Sunday, June 21.
The Electoral Commission of Ghana set Tuesday,July 7 for the by-election after official notification from Parliament last week of Mr Mosore’s resignation.