Aliou Cisse's side - among the tournament favourites - went ahead through Inter Milan forward Keita Balde's low finish after 28 minutes.

Krepin Diatta blasted in a second from the edge of the box with 64 minutes gone as the Teranga Lions dominated.

Senegal are Africa's highest placed nation in Fifa's world rankings at 22nd but have never won the tournament.

Algeria take on Kenya in Group C's other opening match later on Sunday.

Without suspended Liverpool forward Sadio Mane for their opening match, Senegal wasted a host of chances as they peppered their opponents' goal with 24 shots.

Tanzania, making a first appearance in 39 years following their 1980 debut, had goalkeeper Aishi Manula to thank early on as the 23-year-old twice denied M'Baye Niang in the opening six minutes.

Two minutes after slotting in to the bottom corner, Balde should have added the 2017 quarter-finalists' second but blazed over from Ismaila Sarr's cut-back.

Rennes forward Sarr - a persistent nuisance - had a goal disallowed midway through the first half as Crystal Palace's Cheikhou Kouyate was penalised for handball in the build-up, while Badou Ndiaye's ambitious overhead kick flew over the crossbar.

Manula again came to the rescue for Tanzania after the interval, stretching to guide a Diatta header to safety and smothering an effort from Sarr as the 131st-ranked side remained in touch.

But Senegal were untroubled at the back and Club Brugge midfielder Diatta made the points safe for Cisse's side with an excellent first-time strike.

Senegal now face Algeria on Thursday (18:00 BST), while Tanzania take on Kenya later that day (21:00 BST).

Analysis

by BBC Africa's Nick Cavell:

Senegal were far better. They should have scored many more than the 2-0 scoreline suggests.

This Teranga Lions team is the most balanced it has been for a few years. They looked good - but Tanzania made them look excellent.

There will be far tougher tests to come for Senegal. Tanzania tried to be physical but they were reduced to putting in foul after foul to try to stop the Senegalese charge. All this - and Senegal still have Mane come back.