World junior champion Muktar Edris took the race in a time of 13:20.82 and, although Farah crossed the line in the fifth and final automatic qualification spot, it was a comfortable run for the Olympic champion.
Farah’s training partner Galen Rupp finished in fourth spot. Edwin Soi and Isiah Koech made up the other automatic qualifiers from heat two.
The 30-year-old said: "I just had to get the job comfortably done. The body feels good, the rest of the team has been looking after me.
"It would mean a lot to me to be double champion and hopefully I can make my country proud."
Farah won the 10,000m on Sunday for his first World Championships victory at the longer distance, and is bidding to become only the second man after Ethiopia's Kenenisa Bekele to do the long-distance double at both an Olympics and a World Championships in Moscow.
Ethiopia's Hagos Gebrhiwet won the first heat despite almost taking the wrong bus from the hotel and arriving just in time for the race.
"We arrived so late that we went straight into the race without a proper warm up but luckily everything went well," he said.
1. Hagos Gebrhiwet (Ethiopia) 13:23.22 Q
2. Yenew Alamirew (Ethiopia) 13:23.48 Q
3. Bernard Lagat (U.S.) 13:23.59 Q
4. Thomas Pkemei Longosiwa (Kenya) 13:23.94 Q
5. Ryan Hill (U.S.) 13:24.19 Q
6. Elroy Gelant (South Africa) 13:25.07 Q
7. Brett Robinson (Australia) 13:25.38 Q
8. Sindre Buraas (Norway) 13:26.69 Q
9. Zane Robertson (New Zealand) 13:27.89 Q
10. John Kipkoech (Kenya) 13:31.21
11. Phillip Kipyeko (Uganda) 13:33.68
12. Arne Gabius (Germany) 13:34.26
13. Aziz Lahbabi (Morocco) 13:37.75
14. Sergio Sanchez (Spain) 13:52.05
15. Grevazio Mpani (Malawi) 14:15.65
. Abdoulaye Abdelkarim (Chad) DNS
1. Muktar Edris (Ethiopia) 13:20.82 Q
2. Edwin Cheruiyot Soi (Kenya) 13:21.44 Q
3. Isiah Kiplangat Koech (Kenya) 13:22.19 Q
4. Galen Rupp (U.S.) 13:23.91 Q
5. Mohamed Farah (Britain) 13:23.93 Q
6. Dejene Regassa (Bahrain) 13:25.21 Q
7. Othmane El Goumri (Morocco) 13:31.08
8. Ben St Lawrence (Australia) 13:33.64
9. Aelemayehu Bezabeh (Spain) 13:34.68
10. Bayron Piedra (Ecuador) 13:35.38
11. Yuki Sato (Japan) 13:37.07
12. Diego Estrada (Mexico) 13:48.30
13. Rinas Akhmadeev (Russia) 13:58.38
14. Jake Robertson (New Zealand) 14:09.50
. Moses Ndiema Kipsiro (Uganda) DNS