Serge Aurier's miscued cross gave them the lead before the break and Son Heung-Min sealed the victory with a clever header late on.
The football on show was far from the level that saw Stoke City thrashed 5-1 last weekend, but Pochettino was happy with the display, as Spurs prepare to face Premier League leaders Manchester City this weekend.
"I think it's fantastic for us, three victories in a row – so important for us," said Pochettino.
"I'm happy with the performance.
"It's good to feel again that we are in the top four and it's so important to keep this position now."
The Argentine acknowledged his side had received a little bit of luck along the way, but felt it was deserved after controlling proceedings – Spurs finishing with 75 per cent possession.
"The team deserved it, we dominated the game," he added. "We deserved to go to half time winning the game, [the win was important to] believe and fight for the Premier League.
"We created a lot of chances, it's not easy to play when the opponent play in that formation to try only to stop you to play."