The German champions consolidated their position as the top team in the Bundesliga with a second successive league title in May but Jurgen Klopp's young Borussia have yet to leave their mark in the top European competition after finishing bottom of their group last season.
With their group this season also including Real Madrid and Manchester City, the Germans, 1997 Champions League winners, have their work cut out.
Dortmund could not have wished for a more successful dress rehearsal on Saturday when they eased past Bayer Leverkusen 3-0 with yet another dominant home display after going undefeated in the league at their Westfalen stadium for 12 months.
"Obviously it feels good ahead of Ajax to win like that, better than if we had lost 3-0," said Klopp, who was awarded the coach of the year prize on Saturday.
"We will take all our positive points into this game but the Champions League is a completely different competition. We now have set the standard for our games, playing the football that we need to be playing. Now we have to show we can do it every three days."
GERMAN RECORD
Saturday's win also extended their unbeaten Bundesliga run to 31 straight games, approaching Hamburg SV's record of 36 consecutive matches set in 1982/83.
Klopp can draw from a squad of fit players for the Group D game after forward Marco Reus's injury while on international duty last week turned out to be minor.
He could still, however, opt to leave the 17-million-euro signing on the bench at the start to give him some more rest, as he did against Leverkusen.
"There are a lot of busy weeks until Christmas and there is no doubt I will need every single player," said Klopp.
Defender Marcel Schmelzer also looked sharper after his weak performances for Germany in the 2014 World Cup qualifiers this month.
Ajax coach Frank de Boer is eager to instil some self-belief after the 1995 Champions League winners missed out on the knockout phase on the final match day last season because of Olympique Lyon's remarkable 7-1 win at Dynamo Zagreb.
In the Europa League, Manchester United then proved too strong despite a 2-1 win at Old Trafford.
"Last season we could have eliminated Manchester United only the belief came afterwards and that made me angry," De Boer told reporters. "That mind-set has to change and if we are in shape we can beat Dortmund and also Manchester City."
Without striker Kolbeinn Sightorsson, who is out for months after shoulder surgery, De Boer is considering who will be his central striker as he has no real back up for the Icelander.
Midfielder Siem de Jong is expected to start as striker which will give the Dutch champions a completely Danish midfield.
Probable teams:
Borussia Dortmund: 1-Roman Weidenfeller; 26-Lukasz Piszczek, 4-Neven Subotic, 15-Mats Hummels, 29-Marcel Schmelzer; 16-Jakub Blaszczykowski, 8-Ilkay Guendogan, 5-Sebastian Kehl, 19-Kevin Grosskreutz, 10-Mario Gotze; 9-Robert Lewandowski
