Spurs, who lost Harry Kane to a first-half ankle injury, recovered from their last-16 defeat by Juventus on Wednesday, to win convincingly through Son Heung-min’s double and Serge Aurier’s late far-post header.
Dele Alli had earlier levelled for the visitors after Junior Stanislas gave Bournemouth a seventh-minute lead.
“The answer today was perfect after Wednesday,” said the Spurs boss. “I am so pleased – the reaction was important for the team.
“They [Bournemouth] played at a high tempo which was difficult. We conceded an early goal but it was a massive three points for us.
“There is still a lot of work to do, still a lot of things can happen with eight games to go. Big sides are fighting with us to take a position in the top four.”
Bournemouth, who remain 12th, thought they had rescued a point via Callum Wilson’s 84th-minute strike but referee Mike Dean disallowed it for a shove on Spurs defender Davinson Sanchez, before the visitors scored their two late goals.
Alli gave Tottenham fans a scare when he was replaced late on, as did left-back Danny Rose, who was making his first top-flight appearance of the year, but both were fatigued rather than injured.
It was Pochettino’s 150th league win as a manager but a rare recent defeat for his counterpart Eddie Howe, whose side had been beaten just once in their past 10 league fixtures – only Tottenham losing fewer in that period.
