The Dons climb to fifth in the table courtesy of a sixth successive game without defeat at Pittodrie.
Twardzik saved from Goodwillie to prevent Stuart McCall's side going further behind inside 15 minutes, and Niall McGinn could have doubled Aberdeen's advantage when he dragged a shot wide from eight yards.
Motherwell are the lowest scorers in the division with only six goals in 11 games and struggled to create chances. Their best hope of an equaliser was from corners, but McManus skied over the crossbar from close range and Simon Ramsden headed over at the back post.
The visitors showed few signs of a comeback in a dour second half, and Goodwillie could have put Aberdeen further clear when he blazed high at the end of a counter-attack led by Northern Ireland international McGinn.
It took until the 77th minute for Motherwell to have a shot on target, but Craig Reid's skidding effort was easily held by Scott Brown as the second-from-bottom side lost for the fourth game on the bounce.