Beaten finalists in May, and victims to Bayern Munich once again at the weekend, Jurgen Klopp's men had struggled to recreate last season's swashbuckling group-stage performances and found themselves trailing Serie A runners-up Napoli by three points ahead of Tuesday night's encounter.
But an early penalty from Marco Reus gave them the upper hand before second-half goals from Jakub Blaszczykowski and substitute Pierre-Emerick Aubameyang ruled Lorenzo Insigne's response irrelevant.
They now need only match or better Napoli's result against Arsenal when they visit bottom side Marseille in a fortnight to ensure their progression to the last 16.
A tepid start which betrayed the frantic game that followed gave way in the 10th minute when Federico Fernandez unwisely pulled Robert Lewandowski's shirt in the area.
Referee Carlos Velasco Carballo had no choice but to award the penalty, which Reus dispatched to Jose Reina's left with a minimum of fuss.
Dortmund sought to hit their opponents while they were down and, after Lewandowski screwed a shot wide from close range, Reina was forced to make a stunning save and deny Reus from distance.
The resistance allowed Napoli to bite back, Gonzalo Higuain first testing Roman Weidenfeller's reflexes before glancing a Dries Mertens free-kick into his gloves.
Jose Callejon sparked a goalmouth scramble as his sharp strike rattled a post, Valon Behrami stealing onto the rebound only to slam it against Weidenfeller.
Dortmund caught their breath and streaked up the other end, where Reina was waiting to disappoint them with some heroic goalkeeping.
Henrikh Mkhitaryan bent the ball from an improbable angle in the 33rd minute, Reina tipping it round the post at full stretch before defying the odds to block a Lewandowski screamer two minutes later.
Both stoppers were afforded some time to gather their thoughts before the break but it was lucky for Dortmund that Weidenfeller stayed focused until the half-time whistle.
Pablo Armero conjured up the last moment of magic at the end of 45 entertaining minutes, loping down the left wing and blasting with power at the German keeper, who palmed the ball to safety.
Dortmund were the much brighter side when play resumed, though, and a 15-minute onslaught yielded a vital second goal.
Reus had twice tried his luck against Reina to no avail before supplying the killer pass for Blaszczykowski on the hour mark.
The ball that broke the Spanish keeper's resolve was passed in from the left from Reus to Blaszczykowski and the Pole tucked it home with relative ease.
Napoli, however, halved the deficit 11 minutes later.
Higuain had been the biggest threat to Weidenfeller but he instead turned provider for the Italian response.
The Argentinian looked up from his position on the left wing to spot Insigne in good space and the young striker swept the ball into the back of the net.
This was Napoli's opportunity to force the issue but it was a chance they would not manage to take as substitute Aubameyang put the result beyond doubt in the 78th minute.
Lewandowski, who had had a reasonably quiet second half, was perfectly placed to tee up his Gabonese team-mate for an easy conversion in the six-yard box.
In the dying stages, Gokhan Inler and Duvan Zapata both threatened to make an impact from the Napoli bench by driving shots at Weidenfeller, but Dortmund had done more than enough to reignite their push for European glory.