Timur Kapadze fired home the crucial goal 15 minutes before the break following a well-worked move, but Kuruvchi were unable to beat Al Ittihad goalkeeper Mahmoud Karkar as the visitors threatened on several occasions to equalise in the Group A encounter.
But after avoiding several close calls, Kuruvchi remain in contention for a place in the knockout stage after picking up a third win in four games which included a 2-0 win in Syria two weeks ago.
"I’m very happy with win," said Kasimov. "It was a tough match because it was last chance for Al Ittihad. They battled for it very hard - they had nothing to lose.
"We did not convert a lot of goal scoring opportunities. Mahmoud Karkar is a very good goalkeeper and he saved them."
After Server Djeparov and Aleksey Nikolaev both wasted chances to double the lead, Yahia Al Rached should have pulled Al Ittihad level two minutes before the break after being gifted a chance following a slip from Kuruvchi defender Gochguly Gochguliyev, but fired wide.
Karkar denied Gochguliyev after the break, while Mahmoud Al Amena had a chance to equalise for the visitors but pulled his effort wide.
Shavkat Salomov struck the crossbar and Victor Karpenko, Anvarjon Soliev and Salomov were also denied by Karkar in the closing stages as Kuruvchi held onto claim the slender victory.
"We were lucky at the end of first half when Al Rached did not make up pay for Gochguliyev’s mistake," added Kasimov.
"Both halves of match were played at a high tempo."
Despite seeing his side’s chances of reaching the last eight all but disappear after suffering a third defeat in four games, Al Ittihad coach Valeriu Titu was satisfied with his sides performance.
"We had a lot chances and our goalkeeper played very well," he said. "We had at least four chances in both matches but we did not score. That means we have problems converting chances.
"Timur Kapadze and both Kuruvchi central defenders played very well. Their strikers were also very unlucky. Kuruvchi played well in both matches.
"For me, it is my first experience of the AFC Champions League and it has been great."