Second-placed Hamburg, on 21 points, visit Schalke 04, who are third with 19 points, on Sunday while Bayern Munich, in sixth place, host Eintracht Frankfurt on Saturday.
Leverkusen, who are unbeaten this season, threatened twice in the opening minutes through Lars Bender and Toni Kroos but it was Dortmund who struck first in the eighth minute.
Paraguay international Nelson Valdez combined well with Nuri Shahin and floated a sweet cross into the area for Argentine Lucas Barrios to head the visitors into the lead.
It was the first goal Leverkusen had conceded in the league since mid-September.
Juergen Klopp's Dortmund team quickly retreated into their own half after going ahead as the hosts dominated possession but failed to carve out any clear scoring opportunities.
In a scrappy second half, Leverkusen finally broke through the visitors' double defensive line when Friedrich headed the equaliser from a Tranquillo Barnetta corner in the 65th as the home side preserved their unbeaten run this season.
"We put on a lot of pressure in the second half. The players fought hard but overall we did not play well," said 64-year-old Leverkusen coach Jupp Heynckes, who had been due to retire before surprisingly taking over the team this season.
"I am happy with the 1-1, though, because Dortmund showed courage. They deserved to get a point here."
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