Both teams missed chances to score in the opening stages, as Peter Gulacsi was forced into the first save of the match after just four minutes by getting behind Said El Mala’s effort.
Shortly down the other end, Yan Diomande worked himself into a decent position before firing over.
El Mala then squandered another opportunity midway through the first half, as he lashed the ball narrowly wide of the far post from a tight angle.
Meanwhile, Leipzig carried a threat from set pieces as a well-worked corner found Xaver Schlager in acres of space in the box, but an unfortunate miskick meant the golden chance was wasted.
However, the visitors would make no mistake from their next set piece, as David Raum delivered a beautifully whipped ball into the area for Christoph Baumgartner to head home past the onrushing Marvin Schwabe.
Leipzig have now scored the opening goal in 18 of their 21 league games this season as they held a half-time lead.
However, despite taking the lead in their previous two matches, the Red Bulls won neither (D1, L1), and they were fearing a repeat as Cologne equalised just five minutes into the second half.
Isak Johannesson found Jan Thielmann in the box, and he produced a brilliant finish into the top corner, leaving Gulacsi rooted.
Leipzig responded straight away, though as Schlager played Baumgartner through and he turned and smashed the ball into the near post to net his brace.
The Austrian turned into a hero at his own end in the latter stages too as Thielmann threatened to score a brace of his own with a strike that looked to be heading into the bottom corner, but Baumgartner blocked it on the line. Replays after showed that the ball deflected onto his hand, but he was not penalised.
Antonio Nusa almost wrapped up the points for Leipzig minutes later, but his shot came back off the post. Still, the Red Bulls held on for victory to see them climb into the top four, as Cologne were denied a third straight home win.
Flashscore Man of the Match: Christoph Baumgartner (RB Leipzig)