Dortmund s French forward Sebastien Haller celebrates scoring the 5-1 during the German first division Bundesliga football match between Borussia Dortmund and FC Cologne in Dortmund on March 18, 2023. AFP
Donyell Malen and Raphael Guerreiro also got on the scoresheet as Dortmund moved a point clear of Bayern, who visit Bayer Leverkusen on Sunday.
Dortmund stormed into a four-goal lead in the first half through Guerreiro, Haller, Reus and Malen before Davie Selke pulled one back before the break, Cologne's first goal in five matches.
Haller, who has faced criticism for a lack of goals as he continues his return from testicular cancer, latched on to a rebound after 69 minutes to chalk up his first double for Dortmund.
Reus added another just a minute later to seal a thumping win for a Dortmund side missing several first-team players.
The victory was a return to form for Dortmund who suffered Champions League elimination at Chelsea and stumbled to a draw with derby rivals Schalke after starting the year with 10 straight wins.
"It was important to grab the lead atop the table and put some more pressure on (Bayern)," said Reus.
"We've got a great game coming up next," he added, with Dortmund away to Bayern on April 1 following the international break.
Toasting his biggest win as Dortmund coach, Edin Terzic said it would "turn the atmosphere around, which wasn't too great" after the club's recent results.
"There are nine more games in the Bundesliga this season where there's a lot at stake. We're looking forward to it."
Cologne are now winless in five and sit 13th, just six points clear of the relegation play-off spot.
Bochum beat Leipzig
Earlier on Saturday, a second-half goal from Erhan Masovic took Bochum to a surprise 1-0 home win over RB Leipzig, dealing the visitors a blow in their top-four battle.
Looking to rebound after Tuesday's 7-0 thrashing at the hands of Manchester City in the Champions League, Leipzig appeared listless in transition and toothless up front.
Bochum took the lead three minutes into the second half when Masovic latched onto a loose ball in the penalty area and headed past Leipzig goalkeeper Janis Blaswich.
Leipzig midfielder Dominik Szoboszlai had a late chance to equalise but his shot hit the inside of the post and rebounded into the arms of Bochum 'keeper Manuel Riemann.
Bochum coach Thomas Letsch credited the "outstanding" Riemann for helping his side hold on in a "wild last 10 minutes".
Leipzig boss Marco Rose called the defeat "disappointing" and lamented his team's "failure to take (their) big chances".
Bochum's second win in a row pushed them four points clear of the relegation playoff spot.
Leipzig could finish the weekend as low as fifth place should both Union Berlin and Freiburg avoid defeat on Sunday.
An injury-time penalty from Schalke's Marius Buelter cancelled out Arne Maier's second-half goal to snatch a point at Augsburg in a 1-1 draw.
Augsburg looked on track for their fourth 1-0 win in their past five home matches but had Ermedin Demirovic sent off midway through the second half to open the door for Schalke.
Two first-half penalties from Andrej Kramaric and a second-half goal from Ilhas Bebou propelled Hoffenheim to a 3-1 home victory over Hertha Berlin.
The victory was Hoffenheim's first since October, ending a run of eight straight defeats, and moved them from last place to outside the relegation zone.
Elsewhere, a second-half goal from Omar Marmoush earned Wolfsburg a 1-0 win at Stuttgart, keeping their late run towards European qualification alive.
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