Scotland ended a run of two straight defeats when they overcame Luxembourg in their last friendly clash in November, but they had previously failed to win in their last four World Cup qualification matches.
Estonia, meanwhile, were beaten last time out by United Arab Emirates, but they were 1-0 winners over Andorra in their last competitive fixture. They have struggled for goals of late, however, with just two strikes in their previous five matches in all competitions.
Strachan has included Rangers left-back Lee Wallace in the squad, while Chris Burke, James Forrest and Phil Bardsley have also made their returns. Steven Fletcher is expected to return to the attack alongside Jordan Rhodes, with Robert Snodgrass and Kris Commons providing width in midfield.
Estonia will look to Andres Oper to provide their goals on Wednesday as the Nea Salamis striker looks to add to his 38 goals in 130 caps. The 35-year-old is expected to be joined in the attack by Gyori ETO striker Tarmo Kink, who has five goals in 69 caps.
Scotland: Gilks; Bardsley, Berra, Caldwell, Hutton; Adam, Brown, Commons, Snodgrass; Fletcher, Rhodes
Estonia: Pareiko; Sisov, Morozov, Klavan, Jaager; Vassiljev, Purje, Puri, Kams; Oper, Kink
Sports Mole says: 3-1