Sadio Mane and Mohamed Salah had given the Reds a two-goal lead at Stamford Bridge on Monday (AEDT) in their final game before departing for Africa Cup of Nations duty.
Chelsea was not lacking firepower in the absence of dropped record signing Romelu Lukaku as it roared back with two goals in quick succession late in the first half, Kovacic reducing the deficit with a sumptuous volley and Christian Pulisic equalising.
Both sides had their chances to come out on top in the battle between second and third, but it was leader Manchester City that was the big winner as it now holds a 10-point advantage at the summit.
Mane may have been fortunate to only be shown a yellow card when he caught Cesar Azpilicueta in the face with his arm just six seconds into a game that saw the introduction of safe standing at Stamford Bridge.
Pulisic wasted a great chance to open the scoring early on, rounding Caoimhin Kelleher – starting with Alisson out because of a positive COVID-19 test – after Trent Alexander-Arnold's attempted clearance struck Mason Mount and left the United States forward with only the Reds' stand-in goalkeeper to beat.
Mane made no mistake in the ninth minute, capitalising on a bad mistake from Trevoh Chalobah by rounding Edouard Mendy and finishing with his left foot.
Salah then struck against his former club 26 minutes in, exquisitely controlling a brilliant pass from Alexander-Arnold and beating Mendy at his near post with a clinical finish after darting beyond Marcos Alonso in the penalty area.
Chelsea stormed back with two goals in the space of four minutes to go in at the break on level terms, Kovacic's sublime 20-yard volley going in off the right post before Pulisic raced clear and coolly tucked home in stoppage-time.
The two title hopefuls continued to pose a huge threat going forward following the interval and Mendy had to dive at full stretch palm away out Salah's lob when he spotted the Blues keeper off his line.
Kelleher showed sharp reflexes to keep out Pulisic's half-volley and Mount tested the Irishman from long range, but both sides had to settle for a point.