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The home drew level in the first half through Gio Loureiro but United reclaimed their lead before the break and extended it further in the second period.
The result means Coventry sit 15th in the Northern Premier League Midlands table, six points outside of the play-off places and six points above the relegation zone.
Coventry broke the deadlock on 13 minutes when Faulkner lashed a shot into the bottom right corner from 20-yards out.
However, St Ives equalised on 34 minutes as Loureiro smashed a shot into the net via the underside of the crossbar following an almighty scramble in the box at a corner.
United reclaimed the lead in first-half injury time when Palmer headed in a corner from the right to send Coventry into the break with the lead.
And the visitors stretched their lead after the break on 51 minutes as Stone scored from the penalty spot after St Ives goalkeeper Zak Massoud fouled Simeon Cobourne in the box.
Coventry are next in action against Nuneaton Town on Saturday, October 31 with kick-off at 3pm at The Oval.