The Silkmen wore special shirts printed with "Rest in Peace Gaffer" on the back in the minute's silence in Alexander's memory before the kick-off at Edgar Street.
Matt Brown headed inches wide of the post from a Lee Bell free-kick for Macc before they took a 16th-minute lead. Sappleton picked up the ball just outside the penalty area before drilling it past goalkeeper Adam Bartlett into the roof of the net.
Macclesfield continued to push forward and only a block by Bartlett stopped Sinclair putting them further in front in the 32nd minute.
Bartlett also dived full length to push a curling shot from Ross Draper away to safety and seconds later smothered the ball at the feet of Sappleton.
Play continued to switch from end to end and only a spectacular save by Jon Brain stopped Sam Guinne equalising with a 25-yard volley in the 58th minute.
But four minutes later Sinclair weaved his way into the penalty area before landing goalkeeper Bartlett to score from close range to secure Macclesfield's victory.