The 52-year-old Indian chess legend won the Armageddon encounter against Tari after the classical match finished in a 22-move draw.
Anand was made to work hard by Tari in the sudden death tie-break as he needed 87 moves to secure the victory early on Saturday.
He finished with 14.5 points to sign off at the third place behind Carlsen (16.5 points) and Azerbaijan’s Shakhriyar Mamedyarov (15.5).
The Indian GM started superbly, scoring victories in his first three matches (against Maxime Vachier-Lagrave, Veselin Topalov and Wang Hao) and then pulled off an impressive win over Carlsen.
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He led the points table after the fifth round but appeared to lose steam in the second half of the tournament.
A defeat at the hands of Mamedyarov in the Classical in round eight hurt his chances to a large extent.
Anand scored over long-time rival Carlsen in the Blitz event before prevailing over him again in the Classical tournament.
Carlsen was able to finish on top despite not being at his best and suffering defeats to So, compatriot Tari and Anand.
After all classical games on the final day ended in draws, there were wins for Vachier-Lagrave over Anish Giri (the Netherlands) and Anand.
Carlsen had to settle for a draw in the Armageddon against Topalov, while Mamedyarov was held by Radjabov and Wang Hao shared the honours with So.
Final standings: 1. Magnus Carlsen (Norway) 16.5 points, 2. Shakhriyar Mamedyarov (Azerbaijan) 15.5, 3. Viswanathan Anand (India) 14.5, 4. Maxime Vachier-Lagrave (14), 5. Wesley So (USA) 12.5, 6. Anish Giri (12), 7. Veselin Topalov (Bulgaria) and Aryan Tari (Norway) 9.5, 9. Teimour Radjabov (Azerbaijan) 8, 10. Wang Hao (China) 7.5.