Match ends, Hamilton Academical 0, Motherwell 1.
Hamilton Academical head coach Brian Rice says his side "know what they need to do" if they are to defy the odds and secure Scottish Premiership survival.
Victory for Kilmarnock and defeat for Ross County means Rice's men are three points adrift with three games remaining after losing to Lanarkshire rivals Motherwell.
Mark O'Hara's first-half strike was enough to down the 10-man hosts, who saw Ronan Hughes sent off.
"Nothing has been decided," Rice said.
"We didn't deserve to win but I'm disappointed we didn't take something. We need to dust ourselves down and get over the disappointment."
Motherwell's first derby win since August 2019 - coupled with County's defeat at home to St Mirren - means the Fir Park club's top-flight safety is guaranteed.
In their previous two derbies, Motherwell's defence shipped seven goals and they were all at sea again in Hamilton's first venture forward. Scott McMann's deep free-kick found Hakeem Odoffin all alone at the back post, but the former Livingston man cushioned a volley just wide.
Motherwell responded with a set-piece chance of their own, as Ricki Lamie's close-range header was blocked en-route to goal.
The visitors began to take control as Devante Cole's curling effort was tipped behind by Kyle Gourlay but, despite dominating the ball, the visitors failed to create anything of note until Hamilton were reduced to 10 when Hughes lunged in late on Crawford.
Four minutes later, Motherwell had the lead when patient play around the edge of the box resulted in O'Hara arrowing in a fine low finish into the far corner.
Cole struck narrowly wide with a volley just before the break, but Alexander's side rarely threatened in the second period despite having the extra man.
Instead it was Hamilton who came out with intent - something that was sorely missing from their first-half showing - as Bruce Anderson struck straight at Kelly from the edge of the box.
The home side fought on - as we have come to expect from Rice's side - but they ran out of steam in the closing stages as O'Donnell, O'Hara and Cole struck wide for the visitors as they saw the game out.
Man of the match - Mark O'Hara
What did we learn?
We have become accustomed to Hamilton proving us wrong season after season in their quests for survival, but time is running out for Rice's men to turn this around.
As it stands, they are three points adrift with nine to play for and now on a nine-game winless streak.
It's essentially job done for Motherwell in terms of survival. Alexander has done what was asked of him when he came in to replace Stephen Robinson. Now full focus can go into Saturday's quarter-final with Hibernian and the summer rebuild.
What did they say?
Hamilton head coach Brian Rice: "The red card was a turning point, there wasn't much in the game up to then. To go down to 10 men and lose the goal quickly knocked us."
Motherwell manager Graham Alexander: "It was a big win in terms of the league and the fact it's a local derby.
"We haven't done well enough in these games throughout the season. Hopefully that's a reward for the supporters and a thank you for sticking with us."
Motherwell turn their attention back to the Scottish Cup this Saturday as they travel to Hibernian (17:00 BST) in the quarter-finals, while Hamilton go to St Mirren in the league the following week (15:00).
- 5EastonSubstituted forMimnaughat 71'minutes
- 27HodsonSubstituted forThomasat 79'minutes
- 2OdoffinBooked at 7mins
- 15HughesBooked at 33mins
- 34CallachanBooked at 31minsSubstituted forSmithat 68'minutes
- 9LongBooked at 26minsSubstituted forMaguireat 64'minutes
- Kevin Clancy
- Shots on Target
Second Half ends, Hamilton Academical 0, Motherwell 1.
Attempt missed. Devante Cole (Motherwell) right footed shot from a difficult angle on the right is close, but misses to the right. Assisted by Allan Campbell.
Corner, Hamilton Academical. Conceded by Stephen O'Donnell.
Foul by Nathan McGinley (Motherwell).
Nathan Thomas (Hamilton Academical) wins a free kick on the right wing.
Attempt missed. Mark O'Hara (Motherwell) right footed shot from the right side of the box misses to the left. Assisted by Barry Maguire following a corner.
Corner, Motherwell. Conceded by Aaron Martin.
Corner, Hamilton Academical. Conceded by Nathan McGinley.
Substitution, Hamilton Academical. Nathan Thomas replaces Lee Hodson.
Foul by Nathan McGinley (Motherwell).
Hakeem Odoffin (Hamilton Academical) wins a free kick in the defensive half.
Attempt missed. Stephen O'Donnell (Motherwell) right footed shot from a difficult angle on the right misses to the left. Assisted by Mark O'Hara with a headed pass.
Hand ball by Bruce Anderson (Hamilton Academical).
Attempt saved. Devante Cole (Motherwell) right footed shot from outside the box is saved in the centre of the goal. Assisted by Nathan McGinley.
Substitution, Hamilton Academical. Reegan Mimnaugh replaces Brian Easton.
Foul by Mark O'Hara (Motherwell).
Hakeem Odoffin (Hamilton Academical) wins a free kick in the attacking half.
Attempt blocked. Allan Campbell (Motherwell) right footed shot from outside the box is blocked. Assisted by Devante Cole.
Substitution, Hamilton Academical. Lewis Smith replaces Ross Callachan.