- Tag results for Tottenham
Pochettino's side had been under the cosh as Dortmund dominated the first half at Wembley, but Hugo Lloris kept them level with a series of fine saves.
Pochettino has taken to defending his failure to win silverware in almost five years at Tottenham by insisting he values qualification for Europe's elite club competition more highly.
Manchester City remained top, Manchester United moved into the top four and Tottenham are still hanging on.
Tottenham have kept in touch with Manchester City and Liverpool with three successive wins.
Last month Spurs confirmed three more Premier League fixtures as well as the Champions League last-16 home leg against Borussia Dortmund would all take place at the national stadium.
Reus went off after drilling in a superb free-kick, his 17th goal in all competitions this season, in Tuesday's shock German Cup home defeat by Werder Bremen.
Spurs looked to be heading for their first league draw of the season at Wembley but Son's 83rd-minute strike earned Pochettino's men a hard-fought 1-0 win over Newcastle.
Content contenders, money problems for Arsenal, Spurs and Brexit uncertainty all led to a quiet winter transfer window.
Connor Wickham gave the unfancied Eagles, 29 points adrift of Spurs in the Premier League, a ninth-minute lead before a penalty by former Tottenham winger Andros Townsend made it 2-0.
Chelsea will now face holders Manchester City in the final on February 24th.
Arsenal have lost three of their past six Premier League matches to fall six points behind Chelsea in the race for a top-four finish.
Kane sustained the injury to his left ankle in the closing moments of the 1-0 loss at Wembley and scans have now confirmed the extent of the problem.
Kane was hurt after clashing with United defender Phil Jones in the closing seconds of the match as the visitors dug deep to protect their 1-0 lead at Wembley on Sunday.
Goalkeeper David de Gea produces masterclass as Marcus Rashford strike helps Manchester United beat Tottenham 1-0
Interim manager Solskjaer has installed Rashford as his number one striker and was richly rewarded when the 21-year-old scored the decisive goal in the 44th minute.
Rashford looks reborn under interim coach Solskjaer, scoring three times in the centre-forward position as United have rattled off four straight league wins since Mourinho's sacking.