The three judges all scored the fight a 38-38 draw but Taylor avoided her first defeat in four years when two of the judges gave her their deciding vote.
The 28-year-old Olympic champion will now face Estelle Mossely of France in the final on Saturday.
Taylor lost the first round on two of the three judges??? cards but levelled after an exciting second in which her cleaner, more aggressive work paid off.
However, she found herself behind going into the final round after the sharp work of Alekseeva took her ahead once again.
But Taylor then defied the partisan home crowd to pull out a big final round and earn a wafer-thin split decision.
“I know how it feels to lose,??? said Taylor. ???I think it’s important to feel those losses, because I never want to feel like that again.
“I knew I was down after the third round so I had to go out and put the pressure on her and try to win it clearly. The last round was all about heart and thank God I pulled through.
“It was always going to be a close fight because she’s a top boxer but I felt I won a lot of those rounds quite clearly.
“I always go into a fight thinking the decision is going to be fair and I relish these fights where the atmosphere is so fantastic.”
There was more good news for Ireland as Michael O’Reilly advanced to the men’s middleweight final when his scheduled Russian opponent Maxim Koptyakov was forced to withdraw from the competition with an eye injury.
But Belfast lightweight Sean McComb will have to settle for a bronze medal after he was comfortably outpointed by impressive Azerbaijani World No 1 Albert Selimov.