David Watson and Danny Armstrong found the back of the net early in each half for Kilmarnock, dealing a blow to St Johnstone’s hopes of remaining in the William Hill Premiership.
Watson scored his fifth goal of the season in the 12th minute, putting Kilmarnock on the path to a 2-0 victory.
St Johnstone had chances in the first half to equalize, but were unable to trouble Kilmarnock after Armstrong converted a penalty in the 53rd minute.
Saints missed an opportunity to capitalize on Ross County's defeat once again.
With three games remaining, they are six points behind and face a crucial match against Ross County next Saturday.
In a bold move, Valakari handed Uche Ikpeazu his first start for the club, following his return from a long-term knee injury.
Kilmarnock dominated in the attacking third initially, leading to Watson's opening goal.
Despite Saints having chances to intervene, Watson capitalized on a defensive error and put his team ahead.
Armstrong and Fisher prevented Kilmarnock from extending their lead further.
St Johnstone had their chances to equalize, with Kirk and Ikpeazu missing golden opportunities.
However, Kilmarnock took control early in the second half, with Armstrong converting a penalty awarded after VAR intervention.
Despite late efforts from St Johnstone, Kilmarnock's defense held firm.
The win takes Kilmarnock to 41 points, six points clear of the relegation play-off spot.