Spurs had Xavi Simons sent off just past the half-hour mark and Isak then broke the deadlock in the capital with a 56th-minute finish.
Ekitike's header 10 minutes later – his fifth goal in his last three league outings – was enough to secure the points for the Reds, who held on after Richarlison netted late in the second half.
The hosts went down to nine men in stoppage time after Cristian Romero was guilty of a second bookable offence.
Team
Conor Bradley returned from suspension as the only change to the line-up Liverpool deployed against Brighton & Hove Albion the previous weekend.
Jeremie Frimpong started on the bench after recovering from the injury he sustained in October.
Liverpool: Alisson, Van Dijk, Konate, Kerkez, Wirtz (Nyoni, 90+9), Szoboszlai, Mac Allister, Bradley (Isak, 46 [Frimpong, 60 (Chiesa, 90)]), Jones, Ekitike (Robertson, 90+9), Gravenberch.
Unused subs: Mamardashvili, Ramsay, Ngumoha, Lucky.
First half
Clear-cut chances were at a premium in the opening period, even after Tottenham were reduced to 10.
Bradley made an important block on a Randal Kolo Muani shot inside the first five minutes.
Virgil van Dijk headed straight at the goalkeeper before Kolo Muani did the same at the other end.
The flashpoint of the half came when Simons' initial yellow card for a challenge on Van Dijk was changed to a red via a VAR review, with it deemed serious foul play.
Liverpool looked to press home their numerical advantage immediately, Florian Wirtz testing Guglielmo Vicario with a side-footed curler from inside the box.
Second half
Isak came on for Bradley, who took a knock towards the end of the first half, as Dominik Szoboszlai dropped into right-back.
The No.9 was only on the field for 11 minutes but in his final act he put the visitors ahead by thrashing a first-time finish past Vicario, having been played in by Wirtz.
There was no celebration from the scorer, however, as he remained on the ground as a result of being caught by Micky van de Ven in the process.
Spurs nearly levelled when a run from Kolo Muani ended with a strike that took a deflection from Milos Kerkez and floated onto the crossbar.
Two minutes passed and then they were down by two.
Ekitike beat Romero in the air inside the six-yard box to nod home a Frimpong cross that looped off the outstretched foot of Djed Spence.
Richarlison gave the home side hope in the 83rd minute, capitalising on the Reds failing to clear their lines from a corner to halve the deficit.
There were nervy moments in the closing stages, although Liverpool's cause was somewhat aided by Romero receiving his second yellow.
The points were preserved by Alisson Becker intervening on a Pedro Porro shot and threatening cross from Wilson Odobert.