The Magpies have been the better team against the reigning Premier League champions as they look to build on their midweek showing in the Champions League, and had already come the closest to scoring through Harvey Barnes.
That was before Gordon struck at the Kop end to give his side a deserved lead - but Ekitike soon levelled.
Liverpool created the first real opening in the 17th minute when Ekitike turned and let fly from outside the box, but Nick Pope got down to his right to hold.
Moments afterwards, Mohamed Salah raced onto a Dominik Szoboszlai pass from just inside his own half but 35-year-old Kieran Trippier stuck diligently to his task to prevent the Egyptian from getting a strike away.
Trippier, Barnes and Gordon came in for Sven Botman, Lewis Miley and Nick Woltemade as Eddie Howe rotated his squad after the Magpies' draw at Paris Saint-Germain.
In the 26th minute, after Barnes had been brought down by Ryan Gravenberch on the edge of the box, Lewis Hall rolled the free kick into the path of Barnes, whose strike crashed against the woodwork.
Ekitike brought another save from Pope as he was slid through by Gravenberch and went for a chip, but it was beaten away by the Newcastle netminder.
Then came the opening goal as Gordon finished off a superb United move, drilling home right-footed.
Gordon then saw another effort saved by Alisson Becker as Eddie Howe's men pushed for a second - but after good work from Florian Wirtz, Ekitike swept home the equaliser in the 41st minute.
Then two minutes later the Frenchman doubled his tally, drifting in from the left and finishing brilliantly beyond Pope.
Dan Burn continued as captain. The 33-year-old lifelong United supporter was just shy of his second birthday when Newcastle last won at Anfield in the Premier League, with goals from Rob Lee and Andrew Cole giving them a 2-0 win on 16th April 1994.
Newcastle can go above the Reds with victory but will need to do so without regular skipper Bruno Guimarães, who is not risked. He was an unused substitute in Paris but is not fully recovered from the ankle injury which forced him off against PSV earlier in the month.
Sven Botman was also rested as his minutes are managed following his recent return to action.
**Newcastle United:** Nick Pope, Kieran Trippier, Lewis Hall, Sandro Tonali, Anthony Gordon, Harvey Barnes, Malick Thiaw, Anthony Elanga, Joe Willock, Dan Burn (c), Jacob Ramsey
**Subs not used:** Aaron Ramsdale, Sven Botman, Yoane Wissa, William Osula, Jacob Murphy, Nick Woltemade, Alex Murphy, Leo Shahar, Lewis Miley