In 1987 Daugava with Karavajevs as an irreplaceable goalkeeper nearly earned promotion to the [Soviet Top League]] but in 1988 the performance of the club started to decline and Karavajevs had to battle for his position with Valeri Shantalosov.
In 1988 Karavajevs left Daugava for Fakel Voronezh. For two seasons he was the top goalkeeper of Fakel but then he went abroad and joined OFK Belgrade. From Belgrade Karavajevs returned to Latvia where in 1993 he played with Olimpija Rīga. His next move came to Cyprus where Karavajevs played for Evagoras Paphos in 1993/1994. From there his steps lead to Carl Zeiss Jena and FSV Zwickau in Germany.
For the 1998 season Karavajevs went to Latvia as he joined the champion club Skonto FC where he played together with Aleksandrs Koļinko who eventually would replace Karavajevs as the main goalkeeper for Latvia national football team. In 1999 Karavajevs joined the newly-founded FK Rīga with which he won the Latvian Cup and retired after the season.
In total from 1992 to 1999 Karavajevs played 38 matches for Latvia. He never was a 100% first goalkeeper for Latvia, as he had a very strong opponent in the person of Raimonds Laizāns who played for Skonto FC - the base club for Latvia national team in the 90s. Still Karavajevs played slightly more for Latvia - he beat Laizāns by 7 matches but Karavajevs also usually played in the more important matches. Karavajevs played in several historic matches for Latvia - when it managed to hold draws against the Euro 1992 winners Denmark and one of the strongest European national teams Spain. He played his last 2 matches for Latvia in 1999 in two goalless draws against Greece and Albania.