The Spaniard flicked a close-range header past Darryl Flahavan to register his 19th goal of the season in the 99th minute of a tight Millennium Stadium final before Ferguson sealed the win with a second goal in the closing seconds.
It meant heartbreak for the Shrimpers who slumped to their second successive final defeat - having lost by the same scoreline to Blackpool last year.
Steve Tilson's side will now be able to concentrate on winning promotion from League Two while crisis club Wrexham bid to move clear of the bottom four in League One.
The first half was entertaining with Smith's side starting brightly before Southend slowly got back into the game.
However, the second half was a nervy affair and there was little improvement in extra-time as both sides seemed resigned to taking part in the seemingly inevitable penalty shoot-out.
That was until Ugarte struck and after that Southend had little left in the tank to mount a comeback.
Southend were the team in form having gone 17 games unbeaten in their quest to win promotion but they started the game poorly as Wrexham piled on the early pressure.
Wrexham should have taken the lead after just 11 minutes when Ugarte latched on to Steve Roberts' long ball forward but the selfish striker elected to shoot when Chris Llewellyn was completely unmarked to his right.
When Southend hit back Freddy Eastwood almost capitalised on a loose ball inside the Wrexham penalty area before Craig Morgan made a vital clearance six yards from goal.
Southend defender Spencer Prior then forced Ben Foster into a smart save before Mark Jones' superb 25-yard shot sailed just wide for the League One strugglers.
Eastwood then fired just wide for the Shrimpers as the match opened up while Mark Bentley forced Foster to make another smart stop.
The second half was a much more tepid affair but with the match heading for penalties, Ugarte stooped to head Wrexham ahead before Ferguson put the seal on a fine individual display in the last minute.