In the day's other game, Lukas Podolski scored twice in five minutes in the first half to set Cologne on the way to a 3-0 win over struggling Augsburg.
Hamburg, unbeaten in their last three games, climbed to 16th in the 18-team table with nine points from 11 games, swapping places with Augsburg who have eight and are now in the relegation zone.
Bayern Munich, 4-0 winners over Nuremberg on Saturday, lead with 25 points, four clear of Schalke 04.
Hamburg, still winless at home, were in trouble when Serbian defender Slobodan Rajkovic was sent off in the 22nd minute for elbowing Kaiserslautern captain Christian Tiffert, leading to angry protests from their players.
New Hamburg coach Thorsten Fink, whose debut at home to VfL Wolfsburg last weekend also ended 1-1, then made an unorthodox move, taking off striker Marcus Berg, brought in as a replacement for injured Mladen Petric, in the 37th minute.
One minute later, Kaiserslautern, 13th with 12 points, went ahead when Olcay Sahan outfoxed his marker and crossed to Konstantinos Fortounis, who pulled the ball back for Pierre de Wit to score.
De Wit crashed a free-kick against the post after the re-start but feisty Hamburg refused to give in and Paolo Guerrero had a goal disallowed for handball as they fought back.
The Peruvian, however, only had to wait another five minutes before heading Hamburg level on 64 minutes after Gokhan Tore broke free on the right and crossed.
Elsewhere, visitors Augsburg took the early initiative only for Podolski to break the deadlock when he collected the ball, burst past a defender into the area and sent his left-footed shot past Simon Jentzsch in the 19th minute.
He soon struck again, slotting home a penalty after Hajime Hosogai fouled Christian Clemens, to complete his third Bundesliga brace of the season and take his tally to eight.
Slawomir Peszko ended the contest 11 minutes after the restart when he pounced on a mis-hit clearance by Lorenzo Davids to score from close range.
It got worse for Augsburg when substitute Torsten Oehrl was sent off after only 10 minutes on the field for a foul from behind on Sascha Riether.
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