Motherwell finished with 10 men after Jake Carroll was sent off
Motherwell's "brilliant" Scottish Premiership win over Dundee was earned despite a "harsh" late red card for Jake Carroll, said Graham Alexander.
Tony Watt headed Carroll's free-kick into the net against the run of play in the first half to give the Fir Park side back-to-back victories.
Carroll was dismissed for a challenge on Max Anderson with 11 minutes left.
"I thought it was a yellow," said Alexander. "It's an honest challenge. He got some of the ball."
Dundee's Paul McMullan had fired against the bar before they went behind and Jason Cummings came close to a leveller.
But Motherwell held on to move up to fourth with seven points, while Dundee remain ninth on two points.
Dundee manager James McPake said pre-match the Dens Park side were "desperate" to record a first league win since returning to the Premiership and their intent was clear in the early stages.
Concerted pressure culminated in McMullan curling a super effort on to the crossbar.
Frustratingly for the visitors, Charlie Adam went off injured half an hour in, Paul McGowan coming on.
Suddenly Motherwell became an attacking force in the game with Watt released into the box and knocking the ball past the advancing Adam Legzdins only for Dundee to clear.
But moments later Watt found the net, his intelligent header carrying Carroll's deep free-kick into the left corner.
Liam Fontaine nodded wide at a corner as the visitors searched for parity in first-half added time and Jordan McGhee was off target with his header in the second half for the Dark Blues.
Cummings spun on the edge of the box to test Kelly before the game's controversial moment.
Carroll slid in on Anderson and Alexander was visibly upset at referee Willie Collum's decision to brandish a red card.
One further chance came Dundee's way with Lee Ashcroft only able to stab a shot into the arms of Kelly.
Man of the match - Tony Watt
As well as his goal, Watt held the ball up well and won useful free-kicks for his side
What did we learn?
Dundee's dominance of the opening half-hour yielded just one clear chance with the McMullan shot and their second-half efforts lacked conviction.
With Leigh Griffiths heavily linked with a return to Dens Park on loan from Celtic, the experience and presence of such a Scotland international would undoubtedly help their cause.
Motherwell may well lodge an appeal against Carroll's dismissal, with the home players aghast at what they perceived as an overly harsh punishment.
New signing Sean Goss made his debut as a second-half substitute and showed his quality with one dangerous cross and a free-kick from wide on the right that almost caught out Legzdins.
What did they say?
Motherwell manager Graham Alexander: "It's a brilliant win for us. It was a fantastic ball in from Jake Carroll. Tony Watt's made a great run, little deft flick.
"I didn't think we played as well as we have done in the previous weeks. A clean sheet was more than welcome for us."
Dundee manager James McPake: "We were the better team. We knew that if we were going to lose this game, the likelihood was that it'd be a set play.
"This was the best we've played this season and we've come away with nothing, which is frustrating."
What's next?
With domestic football going on hiatus for the international break, Motherwell's next engagement is a home league match with Aberdeen on 11 September (15:00) when Dundee host Livingston (15:00).
