Mulgrew (centre) scored the vital goal at Fir Park
Aberdeen claimed victory after a less than scintillating encounter at Fir Park as Charlie Mulgrew rifled in a free-kick with five minutes left.
The goal sealed Aberdeen's first points of the season after an extremely stuffy defensive performance.
Motherwell enjoyed the better of the play but lacked a cutting edge, while keeper Jamie Langfield pulled off a great save from Paul Quinn's header.
And the Dons claimed their first points to leave Well with none.
The match started at a lively tempo, with both teams showing plenty of commitment, although Motherwell had slightly more of a grip on proceedings.
Their best move came in the ninth minute when a brilliant flick by Stephen Hughes and Fitzpatrick's through-ball found Jamie Murphy in the right channel, but his shot across goal was comfortably held by Aberdeen's Jamie Langfield.
Aberdeen were playing 4-4-2 as manager Jimmy Calderwood switched his system to counter the Motherwell attacking threat but were forced to reshuffle when right-back Zander Diamond, who missed much of Aberdeen's pre-season with a foot injury, limped off after 20 minutes to be replaced by Stuart Duff.
Motherwell gradually increased the pressure, but Scott Severin was keeping a lid on the Motherwell attackers and Aberdeen quickly countered on 29 minutes for their best chance of the half.
Mark Kerr sent the ball to Gary McDonald in the inside left position. McDonald got the shot off his left foot and it was palmed away by Graeme Smith in the Motherwell goal.
Other than occasional forays, Aberdeen were playing a waiting game, often with nine players behind the ball, as Motherwell, who were less than incisive, played short passes among themselves at the back.
As the half wore on, Motherwell began to probe and pressure, but despite Keith Lasley and Paul Quinn exchanging some good short passing, the Aberdeen defence were denying them a way through.
Clarkson engineered a shooting chance despite being surrounded by three white shirts, but his 25-yard effort trickled wide and Motherwell seemed to run out of ideas against a comfortable Aberdeen defence.
Motherwell took the attacking initiative once more in the second half, but Severin again was the rock on which Aberdeen were basing their afternoon, denying the home strikers time and time again with crucial tackles and blocks.
After 58 minutes, Motherwell made a change as Darren Smith came on for Jamie Murphy and, with almost his first touch of the game, Smith slipped and failed to take advantage of a cross.
Motherwell were forced to look to the wide areas, throw-ins and corners to find some way through and Scott Leitch and Mark McGhee were looking annoyed in the Motherwell dugout.
Striker Tommy Wright came on for Aberdeen after 68 minutes and almost scored with his first touch, but Graeme Smith's terrific save denied the debutante and his effort began a period of better play from Jimmy Calderwood's side.
Wright was putting in the challenges with all the enthusiasm of a new boy, getting involved with a headbutting incident, but it was still Severin keeping an experienced head as the game ebbed back and forth between the sides.
However, the game had a dramatic final twist on 85 minutes as Scotland Under-21 international Charlie Mulgrew popped up to plant his free-kick into the bottom left-hand corner of the net from 25 yards, leaving Jimmy Calderwood much more pleased than a frustrated McGhee at the final whistle.
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