Meanwhile, spirits are high for the visitors, who claimed their second major piece of silverware last weekend as they beat Livingston in the Scottish League Cup final.
Hamilton head into Wednesday's match having had a 12-day break since losing 2-0 away at Hibernian, a result which ended their run of three league games without defeat.
Manager Brian Rice bemoaned Jamie Hamilton's 11th-minute dismissal which he felt was a "massive turning point" in the game. The 18-year-old defender was shown a straight red card by referee Craig Napier for a challenge on Martin Boyle, a decision which has since been rescinded by the Scottish FA.
After Ross County's surprise win against Celtic, the Accies are now at the foot of the table, two points behind the Staggies, although Rice's men do have up to two games in hand on the six teams above them.
Hamilton's home form in the top flight has been a concern all season, as they have won just two of their 14 matches played at the Fountain of Youth Stadium, the fewest home victories of any side in the Scottish Premiership.
Since winning back-to-back league games against St Johnstone between February and May in 2019, the Accies have failed to win their last four in the league against the Saints.
With their next three games after Wednesday's clash against teams currently in the top six, securing three points against the Saints would provide a massive boost to Rice's side and would push them out of the relegation zone, up to 10th in the table.
St Johnstone lifted the Scottish League Cup for the first time in their history after Shaun Rooney's first-half header proved enough to secure a 1-0 victory against Livingston at Hampden Park on Sunday.
Head coach Callum Davidson, who was the assistant to Tommy Wright when the Perth outfit won the 2014 Scottish Cup, was emotional after the full-time whistle and expressed his delight for what was a "surreal" and "special moment" for both himself and the club.
The Saints held on to beat the Lions for the second time this month and became the first club other than Celtic to win a major trophy in Scotland since Hibernian's Scottish Cup final triumph in 2016.
St Johnstone now turn their attention back to the Scottish Premiership and head to Hamilton having won five of their last seven visits to South Lanarkshire, including a 5-3 victory in October earlier this season.
The Saints have also won three of their last four away matches in the top flight, beating Kilmarnock, Livingston and Motherwell, scoring eight goals in the process.
Claiming their eighth league win of the campaign on Wednesday night would move St Johnstone up to seventh in the league, 11 points clear of the bottom two and three points behind St Mirren in sixth.
Hamilton Academical Scottish Premiership form: LLDWDL
St Johnstone Scottish Premiership form: DWLWLW
St Johnstone form (all competitions): WLWLWW
Defender Jamie Hamilton will be available to play on Wednesday after his red card against Hibernian was overturned by the Scottish FA.
For St Johnstone, midfielder Murray Davidson remains doubtful after missing the last four matches with a calf problem.
Hamilton Academical possible starting lineup:
Fulton; Hamilton, Odoffin, Easton; Hodson, S. Martin, Trafford, McMann; Callachan; Anderson, Moyo
St Johnstone possible starting lineup:
Clark; Kerr, Gordon, McCart; Rooney, McCann, Bryson, Booth; Melamed; Wotherspoon; Kane
We say: Hamilton Academical 1-2 St Johnstone
Hamilton's need for three points is arguably greater than that of the visitors, with Rice's men hoping to take advantage of their games in hand and move out of the danger zone.
However, St Johnstone, who have lost just two of their last 12 matches in all competitions, are playing with plenty of confidence and have the quality to replicate October's victory at the Fountain of Youth Stadium.
The Saints may be drained from Sunday's impressive Scottish League Cup triumph, but should have enough to seal a narrow win against the Accies on Wednesday.