Tottenham beat Championship side Middlesbrough 2-1 in the third round of the FA Cup on Tuesday night in London.
Middlesbrough scored late in the second half to make for a nervy finish for Jose Mourinho's side after George Saville fired past Paulo Gazzaniga from the top of the penalty area to cut Spurs' lead to 2-1.
With 'Boro pushing hard for an equaliser and a replay, Tottenham held on to their lead to advance to the fourth round of the annual domestic competition for the sixth straight season in a matchup with fellow Premier League side Southampton.
Mourinho made five changes to his starting lineup with Lo Celso and Lamela, who both impressed as substitutes in the 1-0 defeat by Liverpool on Saturday, given the chance to impress.
They did just that although both goals came from poor Boro defending. The 4,000 Boro fans who made the trip south were silenced after two minutes when keeper Tomas Mejias played a risky pass out and Lo Celso intercepted before cutting inside and side-footing home.
Boro almost levelled when Lukas Nmecha left Japhet Tanganga on the ground after a great turn but he was denied by Gazzaniga who had a relatively quiet evening.
Tottenham's second goal was almost a carbon copy with Lamela seizing on some sloppy Boro play before slicing through and finishing neatly with the outside of his left foot.
Mourinho's side failed to turn their domination into more goals and things got edgy late on when Saville's shot evaded Gazzaniga who seemed slow to get down.
"I told my players at halftime if we don't make it 3-0 then if 2-1 we would be in trouble and it happened," Mourinho, who has gone on a nine-match run without a clean sheet for only the second time in his 923-game managerial career.
"We did lots of things well, we conceded the goal, a bit frustrating, but more frustrating was that we did not score three, four or five."