Boss Barry Robson has urged his players to keep the pressure on Hearts in the race to finish third.
The Dons slashed the gap on third-placed Heart to just a single point with a battling 1-0 win against St Johnstone in Perth.
Aberdeen have now won four successive games to pile the pressure on the Tynecastle club.
In contrast Hearts, who lost 2-1 at Kilmarnock, have suffered three straight defeats.
The team that finish third in the Premiership could secure a Euro cash prize in excess of £3 million and continental action until Christmas.
A third-place finish lands a place in the UEFA Europa League play-offs – providing Celtic or Rangers win the Scottish Cup.
Even defeat in the play-offs would see the club that finishes third drop into the UEFA Conference League group stages.
However Robson, who was recently confirmed as manager until the end of the season, warned nothing has been achieved yet.
Robson said: “We showed resilience, kept another clean sheet and won away from home again, which we’ve not done well as a club for years.
“I said to the players we can be better, but get the heads down, keep working, move on.
“We’ve not achieved anything yet.”
Players back from international duty
Aberdeen secured the vital win courtesy of a solitary goal in the 30th minute.
Defender Angus MacDonald’s shot was initially saved by keeper Remi Matthews who pushed the ball out.
However it bounced off Matthews’ foot and into the goal.
Aberdeen played against 10 men for the majority of the match in Perth following the dismissal of Andy Considine after six minutes.
Former Dons defender Considine received a straight red from referee Colin Steven following a VAR review for a last man challenge on Bojan Miovski.
Aberdeen were also reduced to 10 men in injury time when captain Graeme Shinnie received a second yellow for a foul on Drey Wright.
Robson said: “The most pleasing thing was that we were in control of the game.
“I didn’t think St Johnstone were going to score a goal apart from the last five or 10 minutes, which we knew would happen.
“I didn’t want to do anything silly in the game because we were a goal up.
“We probably didn’t switch the ball or play things through quick enough.
“You could see we had boys away on international duty – Duk (Cape Verde) Bojan Miovski (North Macedonia) and Ylber Ramadani (Albania) are big players in the team.
“They didn’t get back until Thursday and Friday so we couldn’t properly match-prep them.”
Half-time message from Robson
Aberdeen have now secured back to back Premiership victories away from home.
Until this two game away winning streak the Dons had not won in the league on the road since October last year.
Aberdeen saw off Dundee United 3-1 last month to end that barren run then followed it up with the win in Perth.
Robson said: “My message to them at half-time was ‘keep a clean sheet’ because if we do that we’ll win the game.
“We’re at the stage in the season where pitches are poor and we need to get points.
“St Johnstone is such hard place to come and play, and that’s credit to Callum (Davidson, manager) and his team.
“Our remit was to come down here and win, and we did.”
Frustration at Shinnie dismissal
Aberdeen did not match the high performance levels of their previous game where they overcame Hearts 3-0 at Pittodrie.
This win was more about resilience, fight and team spirit.
The win was soured slightly late on when Shinnie received a second yellow card in the first minute of time added on.
Robson was left frustrated at the dismissal of his captain.
He said: “Come on, I got a player sent off and it’s never been a sending off.
“VAR can’t even look at that. It’s just frustrating.”
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