Spurs fans must have been thinking 'here we go again' after seeing their side take the lead three times, only for Portsmouth to get back into the game on each occasion.
The memory of Wednesday's embarrassing defeat to Manchester City was still fresh in everyone's mind inside the stadium, but Poyet ensured there would be no repeat performance and helped get Tottenham back to winning ways.
David Pleat handed a debut to new £7million signing Jermain Defoe and the former West Ham marksman wasted no time getting his name on the scoresheet.
Robbie Keane's 12th minute throughball fell perfectly for the England Under-21 star, who made space for himself on the edge of the box, before firing a right-foot shot into the corner of the net.
Tottenham could have an added a second after 24 minutes when Simon Davies burst through into the box, but he saw his shot beaten out by Pompey keeper Shaka Hislop.
Nigel Quashie was desperately unlucky not to level the scores in the 33rd minute when his blistering 25-yard drive flew inches past the post.
But Portsmouth managed to grab an equaliser six minutes later when Stephen Carr's attempt to clear Yakubu Ayegbeni's cross hit Eyal Berkovic and rebounded into the back of the net.
The home side regained the lead just three minutes later when Carr played in Keane and, on the turn, the striker fired a superb half-volley past Hislop.
Portsmouth came out for the second half determined to get themselves back into the game and Ayegbeni's 56th minute drive produced an excellent save from Kasey Keller, diving to his left.
Pompey got their just rewards when they drew level once again 18 minutes from time, when new signing Lomana LuaLua somehow managed to elude two challenges on the edge of the box and curl the ball into the corner of the net.
Tottenham refused to lie down and got themselves back in front once again seven minutes later when Keane grabbed his second of the game.
The Republic of Ireland international forced his way into the penalty box and weaved past two defenders before lifting the ball over Hislop.
Home fans must have started to have nightmare visions of that FA Cup defeat when Portsmouth came back from the dead once again, to equalise for a third time.
Ayegbeni's cross fell perfectly for Ivica Mornar to net his first goal for the club with only six minutes left to play.
But just when everyone looked to be content with a draw, Poyet popped up in the 89th minute to send the White Hart Lane faithful into raptures.
Davies' corner was headed back by Dean Richards and the Uruguayan made no mistake when bundling the ball home from close range.
Acting Spurs boss Pleat said: "I am delighted to win in what has been a traumatic week for the club.
"Fortune went for us today and football is full of irony. I thought Portsmouth played really well and good luck to Harry Redknapp and Jim Smith for the rest of the season.
"I never thought 'here we go again' when Portsmouth came back into the game and felt we took a lot of unfair stick after the FA Cup defeat.
"But we showed great perseverance and both Keane and Defoe looked really sharp in our attack."
Man of the Match: Robbie Keane produced another top class display, scoring twice and creating one for his new strike partner.