The visitors looked set for a 1-0 defeat at the Liberty Stadium thanks to an early goal from Wayne Routledge, but turned the game around in the dying minutes to secure a win that keeps them seven points behind leaders Chelsea in the table.
Dele Alli equalised in the 88th minute before Son Heung-min and Christian Eriksen scored in stoppage time to secure a fifth victory in a row in the top flight for Spurs, who were without Harry Kane, Danny Rose, Hugo Lloris and Victor Wanyama in south Wales.
Manager Pochettino admitted that his players had been complacent early on, but believes they showed their determination to fight for silverware with their spirited late effort.
"We started the game well and created chances in the first few minutes. We maybe feel that the game is going to be easy," Pochettino told BBC Sport.
"They started to play at a low tempo. When we conceded we realised we needed to improve our level.
"It is crazy how the goals came in the last few minutes but we pushed and we created chances to win. It was a difficult game and the team showed big character.
53 - Since M.Pochettino was appointed as boss, Spurs have won 53 points from losing positions in the PL; 13 more than any other side. Battle— OptaJoe (@OptaJoe) April 5, 2017
"The most important thing is the badge. When you play for Tottenham it is not about the names, it is about the team. This season we are showing that we are a team.
"I don't care what people say or what people think of the history of the club. This season we are fighting again. We are in a good way."