Salvation in Islam
Ehteshaam Gulam

In Islam every Muslim who accepts faith will gain salvation (enter Heaven):

Narrated Anas: I heard the Prophet saying, "On the Day of Resurrection I will intercede and say, "O my Lord! Admit into Paradise (even) those who have faith equal to a mustard seed in their hearts." Such people will enter Paradise, and then I will say, 'O (Allah) admit into Paradise (even) those who have the least amount of faith in their hearts." Anas then said: As if I were just now looking at the fingers of Allah's Apostle. (Bukhari Volume 9, Book 93, Number 600)

The Quran also makes it clear that Muslims who have faith and do good works enter into heaven:

But those who have faith and work righteousness, they are companions of the Garden: Therein shall they abide (For ever). (Quran 2:82)

If any do deeds of righteousness,- be they male or female - and have faith, they will enter Heaven, and not the least injustice will be done to them.  (Quran 4:124)

Those who believe, and work righteousness,- their Lord will guide them because of their faith: beneath them will flow rivers in gardens of bliss. (Quran 10:9)

That He may reward those who believe and work righteous deeds, out of his Bounty. For He loves not those who reject Faith. (Quran 30:45)

Those who have faith and do righteous deeds,- they are the best of creatures. Their reward is with Allah: Gardens of Eternity, beneath which rivers flow; they will dwell therein for ever; Allah well pleased with them, and they with Him: all this for such as fear their Lord and Cherisher. (Quran 98:7-8)

Of course there are many other references, but I think for now, thesewill suffice. So we can see that Muslims do have the promise of Salvation.