It looked like they would leave empty-handed when Michael Harriman and Garry Thompson netted within the space of three first half minutes.
But Lavery grabbed a lifeline just before the interval before Webster levelled with a thumping header after it.
Paul Cook made one change to the side that romped to a 6-0 victory over York during the week.
Adam McGurk came into the attacking three behind lone striker Lavery, with Gareth Evans dropping to the bench.
Jayden Stockley was also named among the substitutes having missed the last nine games with an ankle injury.
There was not much excitement to warm the crowd up in the opening stages, with chances at a premium.
Marc McNulty could only head a Ben Davies free-kick wide, while Danny Hollands was forced to divert a corner over his own crossbar at the other end.
The hosts tried to liven things up with a clever free-kick routine midway through the first half, but after Sam Wood cheekily flicked the ball up, Paul Hayes could only fire into the wall.
Wycombe were gifted the lead on 28 minutes, however, when Brian Murphy charged from his box and sent a clearance straight to Luke O’Nien.
The midfielder’s effort was blocked, but the ball fell to Harriman, who calmly finished from 30 yards with Pompey’s keeper yet to get back into position.
And things soon got even worse for the visitors as, less than three minutes later, Harriman got clear down the right and swung in a dangerous cross that Thompson fired home.
The Blues tried to hit back, with Lavery and Kyle Bennett both denied by some last-gasp defending from the Chairboys.
But it took a fine stop from Murphy to stop them falling further behind on 38 minutes, with the keeper spreading himself to deny Wood from point-blank range.
Pompey had been well below-par, although they finished the half with a flourish and Aaron Pierre diverted Enda Stevens’ low cross just past his own post.
And the visitors grabbed a lifeline in stoppage-time after McNulty beat the offside trap to latch onto Christian Burgess’ threaded pass and unselfishly squared for LAVERY to slot home.
Wycombe Wanderers 2
Cook made a switch at the start of the second half, with Hollands making way for Adam Barton in midfield.
Pompey soon had a chance when Davies delivered a free-kick into the area, but Wycombe were able to scramble clear and referee Mark Haywood ignored Webster’s pleas for a penalty.
WEBSTER was celebrating on 55 minutes, however, when he was left unmarked to convert Davies’ corner with a bullet header that was too powerful for Chairboys keeper Matt Ingram to keep out.
Hayes had his own chance from a set-piece moments later, but he could only divert the ball straight into Murphy’s arms.
The Blues then surged straight down the other end and Pierre made a decent block to keep out McGurk’s effort.
Cook made his second switch on 67 minutes, with Evans getting a chance to impress in place of McGurk.
He soon made an impact, but after ghosting in at the near post, was unable to divert a corner from Davies on target.
And Evans was in the thick of action again moments later, only to be denied by a vital Anthony Stewart block after Lavery had done well to hold the ball up.
Bennett was next go close when he cut along the edge of the box before firing in a shot that Ingram did well to beat away.
And Burgess thought he should have been awarded a penalty on 84 minutes after going to ground under Pierre’s challenge while trying to attack a corner.
Pierre then fouled Lavery right on the edge of the box and Davies’ free-kick was pushed clear by Ingram.
It was Pompey who were doing all the attacking as the game entered its closing stages, but they were unable to find a late winner.
Wycombe (4-4-2): Ingram; McCarthy, Stewart, Pierre, Jombati; Harriman (Kretzschmar 90+3), Bloomfield, O’Nien, Wood; Hayes (c) (Amadi-Holloway 81), Thompson
Goals: Harriman 28, Thompson 30
Booked: McCarthy, Pierre
Subs not used: Richardson, Rowe, Banton, Sellers, Ugwu
Pompey (4-2-3-1): Murphy; Davies, Burgess, Webster, Stevens; Hollands (Barton 46), Doyle (c); McGurk (Evans 67), McNulty, Bennett (Tollitt 89); Lavery
Goals: Lavery 45+2, Webster 55
Subs not used: Bass, Clarke, Chaplin, Stockley
Referee: Mark Haywood
Attendance: 5,816 (1,976 Pompey fans)