Undefeated Leverkusen, who are on 32 points, four ahead of Werder Bremen and Schalke 04 who play each other on Saturday, thought they had won it when Burak Kaplan's deflected shot gave them a 2-1 lead in the 90th minute.
Ramos, who had given the hosts the lead on eight minutes, headed in a Raffael corner on the final whistle to grab a point for bottom-placed Hertha, who were reduced to 10 men when Gojko Kacar was sent off 13 minutes from time with a second booking.
"We should have held on to that 2-1," Leverkusen's Toni Kroos, who had equalised in the 76th minute, told reporters.
"We basically have our first-half performance to blame for not winning tonight."
Leverkusen looked a shadow of their usual sparkling selves and quickly fell behind when 23-year-old Ramos combined well with Cicero when the visitors' defence was caught napping, chipping the ball over keeper Rene Adler for an early lead.
Lacklustre Leverkusen, who had failed to mount a serious assault on Jaroslav Drobny's goal until then, grabbed a surprise equaliser when Kroos fired in from 16 metres with the Hertha keeper's sight blocked by his defenders.
In the 90th minute Kaplan, in his first Bundesliga match, shot on goal and Hertha's Lukasz Piszczek deflected the ball into the net to give the visitors the lead before Ramos denied them the three points with a well-taken header seconds before the end.
"Just one point is not enough for us now," said Hertha keeper Drobny. "We play Bayern next week and that will be extremely tough."
