Vijender outclassed Trinidad and Tobago's Aaron Prince in men's 75kg category.
The 2008 Olympic bronze medallist won 3-0 on points in an unanimous decision of the three judges.
The first round was a bit subdued with both the boxers trying to get a measure of each other. Vijender played a bit defensively and Prince attacked more.
One judge out of three gave 10-9 points to Finch while the other two gave in favour of Vijender with identical scores.
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Earlier, experienced Laishram Sarita Devi and young Pinki Jangra reached the semifinals of the women's light (57-60kg) and 51kg boxing competition respectively.
World No. 3 L Devendro Singh outclassed Aqeel Ahmed of Scotland to advance to the medal round and so was Mandeep Jangra.
Sarita Devi, the 32-year-old from Manipur, came from behind to outsmart Charlene Jones of Wales 3-1 in a hard-fought quarterfinal bout. She will next take on Mozambique's Maria Machongua in the semifinals on Friday.
In men's 69kg division, young Indian boxer Mandeep Jangra also assured himself of a bronze in his debut Commonwealth Games by advancing to the semifinals after his opponent failed the medical test ahead of their quarterfinal bout.
The Asian Championships silver-medallist, who has won two rounds so far in the event, will now be up against the winner of the clash between Canadian Custio Clayton and Northern Ireland's Steven Donnelly.