Portugal international Guerreiro struck in each half to help the Bundesliga leaders dispose of their hapless hosts and leapfrog Atleti, held to a goalless draw against Club Brugge, thanks to a superior head-to-head record.
Dortmund's largely straightforward win was achieved despite Lucien Favre resting nine members of the team that triumphed 2-1 over Revierderby rivals Schalke on the weekend.
Chances were scant after they went ahead in the 15th minute, but top spot and a fifth clean sheet in six Champions League engagements made for a successful trip to the principality.
Favre's changes eroded none of his team's rhythm and it was no surprise when Maximilian Philipp squared for Guerreiro to tap in the opener.
Monaco, though starved of possession and territory, were unfortunate not to be awarded a spot-kick midway through the half, Sofiane Diop's cross striking Abdou Diallo's arm.
They were soon pressed back into defence and ex-Monaco man Diallo should have extended the margin, but the defender steered wide from Guerreiro's first-time ball across the face of goal.
Another chance came and went for Thierry Henry's team moments after the restart as Kamil Glik headed Youri Tielemans' corner over the bar at close range.
It proved their final real hope of avoiding a seventh successive European home defeat at the conclusion of a forgettable continental campaign, Dortmund's decisive three points confirmed with Guerreiro sweeping home Christian Pulisic's cut-back via a deft Paco Alcacer touch in the 88th minute.
What does it mean? Job done for Favre
It was brave of the BVB boss to shuffle his pack so heavily with top spot still in sight and yet, as with so much of their season to date, it all went according to plan thanks in no small part to Club Brugge's stubbornness in their match with Atletico Madrid.
Top spot secured in Group A and seven points clear in the Bundesliga – Dortmund have bounced back from their struggles last season in emphatic fashion so far in 2018-19, while struggling Monaco can now fully focus on avoiding a disastrous Ligue 1 finish after their misery in Europe.
1 - Monaco have become the first team to fail to win a single group stage game in two consecutive seasons of the Champions League since Dinamo Zagreb in 2011-12 and 2012-13. Oops. pic.twitter.com/bALNHAoFGt— OptaJean (@OptaJean) December 11, 2018
Guerreiro makes push for more minutes
He has played a bit-part role domestically this term but the effervescent Guerreiro continues to relish Champions League opportunities, his third and fourth goals of the campaign capping a highly effective performance on the left flank that saw him create four chances for his team-mates and gain possession 14 times – more than anyone else on the pitch.
Falcao flails up front
Twice on target in the crucial recent win over Amiens, a subsequent weekend off due to protests in France did few favours to Radamel Falcao, who was off the pace at Stade Louis II and wasteful with his rare glimpses of goal, failing to work Marwin Hitz from three attempts at goal.
Key Opta Facts:
- Monaco have failed to win a single group-stage game in two consecutive seasons of the Champions League (D3 L9) – the first side to do so since Dinamo Zagreb (2011-12 and 2012-13).
- Monaco's seven successive European home losses have seen them score only three goals whilst conceding 17. Before this run, they had never previously lost more than two European home games in succession.
- Dortmund have conceded just twice in the group stages this season, the least they have ever conceded at this stage of the competition.
- Dortmund will finish top of their group for the fifth time in their last six Champions League campaigns.
Monaco, though victorious in their last Ligue 1 outing, are likely to find life difficult away to Lyon on Sunday, while in-form Dortmund are sure to welcome back several stars for Saturday's home meeting with Werder Bremen.