The match ended on a sour note, however, as Clifford Mulenga was sent from the field after a confrontation with Tyren Arensde in the dying seconds.
The win sees Celtic up to eighth, while Santos remains in 14th place, just above the relegation zone.
The first 45 minutes was a half dominated by Celtic, as they saw 60 percent of the ball, but they were wasteful in the final third of the field, either being unable to unlock the Santos defence or by attempting long range efforts on goal.
In fact, the first real chance went the way of the visitors in the 19th minute, and it was their only decent effort of the half; a speculative 30-yard shot from Tyren Arendse that went inches wide of the right-hand upright.
After that it was all Celtic and they came the closest to breaking the deadlock on the half-hour mark, when Mulenga curled a 25-yard free-kick around the defensive wall, but his effort was saved by Pa Dembo Touray, who tipped the ball around the post in acrobatic fashion.
From the resulting corner a completely unmarked Erick Mathoho should really have given the home side the lead, but he headed wide from four yards out.
The half ended 0-0.
Celtic continued where they left off in the second half, and Santos looked to be chasing shadows. In the 52nd minute only the brilliant keeping of Touray kept the People's Team on level terms.
Letladi Madubanya broke through the Santos defence on a charging run, but the keeper was quickly off his goalline to smother the attack and grab the ball.
15 minutes later Mulenga worked his way into the left-hand side of the 18-yard box with some sublime skill, but his powerful 16-yard shot was palmed over the crossbar by Touray.
In the 70th minute Mulenga was in the thick of the action again and came close to breaking the stalemate, but his shot shaved the right-hand upright with the keeper well beaten.
Four minutes later Celtic made their pressure pay. A timid low cross from the right, which looked harmless enough, was superbly stuck away from 10-yards out by Osei, to hand Celtic the lead.
Santos tried to find their way back into the match, but it was not to be as they went a second goal down in the 92nd minute – Motshegwa finding the back of the net from just inside the box.
The match, though, did end on a low Mulenga was shown a red card for a confrontation with Wayne Arendse.