A roundup of Saturday's SPFL Premiership results
Hearts defeated Celtic in the early kick-off, while Hamilton won the Lanarkshire derby.
Craig Levein led Hearts to victory over the champions at Tynecastle for the second season in a row, with Kyle Lafferty scoring the goal that sank Celtic.
Brendan Rodgers made sweeping changes to his side ahead of the crucial Champions League match against AEK Athens, but found his side edged out by Hearts in a hard-fought game.
Lafferty struck in the 56th minute with a volley from the edge of the box to give his side six points from six. However, there was also cause for concern for the Jambos when captain Christophe Berra was carried off in the first half with a hamstring injury that could rule him out for some time.
Levein admitterd after the match that the changes to Celtic's strongest side had given him confidence his team could deal them a blow.
"I don't know what Brendan thought but he had serious decisions to make, the Champions League is worth a helluva lot more money to him than beating Hearts away from home.
"I am absolutely positive he could do both but today he did make changes and it was another thing, along with our form, along with recent performances here against Celtic; positive thoughts for us to go into the game absolutely believing we had a chance of winning."
Rodgers said: "Three game in seven days is very tough but not an excuse. We have to be able to cope with that. One mistake cost us".
Gary Mackay-Steven scored from the spot to continue Aberdeen's run of wins against Dundee.
Both sides created plentiful chances in the first half in an open match that couldn't deliver goals with Kharl Madianga, Andy Considine, Sofien Moussa and Stevie May all spurning opportunities to score.
The wastefulness continued into the second period but with fifteen minutes left, Aberdeen were given a spot-kick and the perfect opportunity to get in front.
Nial McGinn's corner was headed by Dom Ball and seemed to be blocked by Genseric Kusunga, prompting Bobby Madden to point to the spot.
Mackay-Steven found the corner with his penalty and gave the Dons three points to build on the draw against Rangers on opening day.
Livingston and Kilmarnock played out a goalless draw at Almondvale, with neither side able to make the most of the few chances created.
Steven Lawless went close to opening the scoring in the first half but saw his effort saved by Jamie MacDonald before Chris Burke hit the post for Kilmarnock.
Stephen O'Donnell had the best chance of the second half but Liam Kelly was equal to it and though the visitors pushed in the latter stages, Livi held on to take their first top-flight point in 12 years.
Hamilton took bragging rights from the Lanarkshire derby as Steven Boyd made an instant impact to give his side the win at Fir Park.
With the game goalless , Hamilton boss Martin Canning made a double substitution, introducing Boys and Ross Cunningham in the hope of finding a breakthrough.
He was rewarded instantly when Boyd scored a volley from 25 yards with his first touch of the game.