Nepal dominated the match but their failure to convert their possession and dominance into goals cost them dearly as Rasheed struck in the 51st minute with a rare opportunity for the tournament debutants.
Having lost their Group A openers, with Nepal going down 2-0 to Palestine and the Maldives losing 3-1 against Turkmenistan, a defeat for either side in Saturday's fixture at the Dashrath Stadium would end their chances of a top two finish and a place in Friday's semi-finals.
Nepal coach Graham Roberts made two changes from the side the lost to Palestine with goalkeeper Kiran Chemzong, whose error led to the West Asians' opening goal, being replaced by Ritesh Thapa and midfielder Nirajan Khadka making way for the more dynamic Bhola Silwal as the home side looked to dictate the pace of the game.
The Maldives were without Ahmed Thariq following the New Radiant striker's sending off against Turkmenistan but in returning captain Ali Afshaq they had a more than capable replacement.
The Maldives' first threat came in the sixth minute when Rabin Shrestha fouled the lively Ashfaq but the free-kick curled in by Mohamed Umair flew just above the peroxide blonde head of the Maldivian skipper.
Ashfaq was again involved in the Maldives' next attack ten minutes later when he subtly slipped the ball through to Hassan Adhuham but his shot from inside the area was well saved by Ritesh.
Nepal almost took the lead in the 29th minute when Mohamed Sifan was caught dithering in defence allowing the industrious Anil Gurung to ghost in and intercept the Victory defender's back-pass to keeper Imran Mohammed, who thwarted the danger when he blocked Ju Manu Rai from close range after a moment of panic in the Maldives defence.
The home side piled the pressure on the increasingly nervous Maldives back line and midfielder Raju Tamang rattled the underside of the cross bar in the 36th minute before Mohammed kept the score line goalless with a superb double save three minutes later, first from Rai's angled drive and then from Bharat Khawas as he attempted to fire in the rebound from close range.
The half-time whistle from referee Dimitri Mashentsev gave the Maldives some relief from the unrelenting Nepal pressure and while the pattern continued at the start of the second half it was the Maldives that took the lead against the run of play, with Mohamed Rasheed capitalising on some slack Nepal defending to fire the ball low past Ritesh and in off his left-hand post.
Nepal pressed for the equaliser but found the Maldives' defence far more solid than they were in the first half and the home side were looking vulnerable on the counter-attack as Ashfaq proved in the 71st minute when he stole possession from Silwal only to see his shot blocked by a quickly recovering defender.
Nepal's attacks were becoming more and more frenetic as the crowd became more and more vociferous and the masses at the Dashrath Stadium thought they were celebrating an equaliser only to see Rai's goal-bound shot blocked on the line in the 78th minute.
Despite laying siege to the Maldives defence for the remainder of the match that would be the closest Nepal came to the equaliser as the hosts' went down all guns blazing in an effort to keep their AFC Challenge Cup hopes alive.