With both sides already eliminated from Group K, just pride and third place were on the line in Tiraspol on Thursday night and it was the hosts who emerged with the points as first-half goals by Cadu and Ismail Isa secured a low-key 2-0 win.
Defeat for Norwegian minnows Tromso sees them finish bottom of the group with just one point from six games, while Sheriff finish two points behind Anzhi Makhachkala, who were well beaten by runaway group winners Tottenham in the night's other game.
The Moldovan hosts wasted little time asserting their authority over their visitors from the Arctic Circle, opening the scoring with just four minutes gone as Cadu headed in from close range from Henrique Luvannor's cross.
Tromso had no response after going behind and fell further adrift in the 36th minute when Benjamin Balima's cross came through to Isa and he had a simple task to tap the ball home six yards.
Tromso finally threatened in second half and were only denied a goal when Vjekoslav Tomic produced a brilliant save to keep out Adnan Causevic firm header from Thomas Drage's corner.
The hosts might have made the margin of victory more comfortable in the final minute when Isa rose to plant a header towards goal but the ball sailed just wide of the target.