Caio Lucas hit the fortuitous winner seven minutes from time after Meloni scored with a 76th-minute header to cancel out an own goal by Kouame Kouadio that gave Oman a 12th-minute lead.
The win moves the UAE to the cusp of their first appearance at the World Cup since 1990 with Olaroiu's team only needing a draw away to Qatar on Tuesday to progress as winners of Group A in the fourth phase of Asia's preliminaries.
The Omanis threatened in the early exchanges when Issam Al-Sabhi stole possession inside the UAE half only for the attack to fizzle out when his shot was eventually blocked. But it was not long before Carlos Queiroz's side had taken the lead.
Ali Al-Busaidi's cross from the left flew across the area to the feet of Amjad Al-Harthi, whose shot took a deflection off Kouadio's heel to beat goalkeeper Khalid Eissa low to his left.
Harib Abdalla's introduction at the start of the second half injected much-needed urgency into the UAE attack, with the forward twice calling keeper Ibrahim Al-Mukhaini into action.
With 14 minutes remaining, the UAE deservedly pulled level, with Meloni rising highest to meet substitute Ali Saleh's inswinging cross from the left to beat Al-Mukhaini.
Seven minutes later, Caio Lucas scored the winner, sending in a cross from the left that swung towards goal, bouncing on the turf inside the six-yard box and skipping beyond the keeper to earn the UAE all three points.
The loss ends Oman's hopes of automatic qualification but the Gulf state could still advance to another round of playoffs if the UAE defeat the Qataris by a large enough margin.
Japan, South Korea, Australia, Iran, Uzbekistan and Jordan have already taken six of Asia's eight guaranteed spots at next year's 48-team World Cup.
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