Queen's Park moved to the top of Scottish League One following a 1-0 win at Falkirk.
Simon Murray scored the only goal in the 36th minute with a fine free-kick, taking his tally to five goals in seven games.
Falkirk had an excellent opportunity to level seven minutes into the second half when they were awarded a penalty after Aidan Kenna was fouled but Callumn Morrison's effort hit the bar.
Montrose were knocked off the top after seeing their unbeaten start to the season come to an end following a 2-1 home defeat to Dumbarton.
Gregor Buchanan, a summer signing from Queen of the South, turned Callum Wilson's free-kick in at the back post to put the Sons ahead in the 20th minute.
Kalvin Orsi, with his first goal for the club, added a second 10 minutes later before Cammy Ballantyne hit the post for Montrose in the second half.
Graham Webster halved the deficit with six minutes remaining from the penalty spot after Andrew Steeves was brought down by Edin Lynch.
Goodwillie struck his fifth goal of the season in the eighth minute after being played through on goal by Conrad Balatoni.
He doubled his tally two minutes before the break, scoring at the second attempt after his initial shot was parried by Kyle Gourlay
Rory McAllister gave Cove some hope with an 84th-minute penalty but Clyde held on despite having Matthew Elsdon sent off in stoppage time.
East Fife climbed off the foot of the table at the expense of Peterhead after winning the basement battle 3-0 at Bayview Stadium.
The Fifers opened the scoring three minutes into the second half when Kevin Smith converted a Jamie Semple cross.
Semple was then fouled by Jason Brown in the box which enabled Connor McManus to double the home side's lead from the penalty spot in the 62nd minute.
East Fife wrapped up the points and their first league win of the season with three minutes left when Danny Denholm turned in a cross from Andrew Osei-Bonsu.