Son Heung-min's thunderous finish helped Tottenham Hotspur secure a 2-0 victory at Leicester City and Liverpool eased past fourth-tier Exeter City 3-0 in FA Cup third-round replays on Wednesday.
Son, who rifled home the opening goal after 39 minutes, set up Nacer Chadli for the second with a beautiful pass in the second half as the eight-times Cup winners eased through against surprise Premier League high-flyers Leicester.
Liverpool scored early through Joe Allen, but then made heavy weather of their lower league opponents and did not add to their lead until substitute Sheyi Ojo curled home superbly.
Joao Teixeira rounded off a comfortable victory for Juergen Klopp's side with a neat near-post finish eight minutes from time.
After the first meeting between Tottenham and Leicester had ended in a thrilling 2-2 draw and with both teams harbouring hopes of challenging for the Premier League title, their managers showed where the FA Cup ranks in their priorities.
Both made a raft of changes to the sides they fielded at the weekend and left out their principal attacking weapons, with Jamie Vardy warming the Leicester bench for most of the match and Harry Kane starting on the sidelines for Spurs.
The game began at a pedestrian pace and only sprang to life after 39 minutes when Son finished emphatically, thumping the ball into the top corner past Kasper Schmeichel as the Leicester defence retreated.
Demarai Gray tested Spurs keeper Michel Vorm at the start of the second half with a curling effort, but Leicester struggled to find any momentum and fell further behind after 66 minutes.
The ball found its way through to Son, who slid a perfectly-weighted through ball for Chadli to calmly finish past Schmeichel and round off a pleasing display for Tottenham manager Mauricio Pochettino.
"The performance was fantastic," he told the BBC. "We played well from the beginning to the end. I think we deserved this victory."
Liverpool manager Klopp introduced a smattering of experience to the side that drew 2-2 at Exeter, in the shape of Allen, Jose Enrique and Christian Benteke, but it was still populated mostly by academy graduates.
One of those, Brad Smith, made a telling contribution as seven-times winners Liverpool took the lead after 10 minutes.
The 21-year-old Australian exchanged passes with Benteke and drilled his low cross into the box for Allen to side-foot home.
The second half was as one-sided as the first and with a similar outcome as Liverpool pressed and dominated but failed to find the killer blow.
While the hosts' struggles to extend their advantage added to the tension inside Anfield, the second goal was worth waiting for as Ojo strolled into the area before beautifully curling his finish into the roof of the net.
That effectively ended any hopes of an upset and was swiftly followed by a third goal as Teixeira was fed through by Benteke and calmly slotted home, allowing Klopp to sing the praises of his young players.
"They showed they are talented with really big skills," he told BT Sport.
Spurs travel to third-tier Colchester United in the fourth round and Liverpool host Premier League rivals West Ham United.
