Macclesfield Town 0 Bournemouth 2
Alexander, 51, collapsed on Friday night and was vomiting but still made it to the ground the following day.
However, on the advice of the club doctor after feeling unwell he went for a brain scan.
Alexander had suffered a brain aneurysm in November 2003 and though he was later given the all-clear, the news seemed to have affected his players as they went through the motions against the Cherries
The visitors should have opened the scoring on eight minutes when Mark Molesley sprang the offside trap only to see his 15-yard drive blocked by the legs of Macclesfield keeper Jon Brain.
Macclesfield's only chance in the first half came on the 17th minute when winger Danny Thomas stung the hands of keeper Shwan Jalal with a drifting 20-yard drive.
Bournemouth took the lead on 50 minutes when Brett Pitman found ex-Man City striker Lee Bradbury, now playing right back, at the far post.
Bradbury rediscovered all his old striker's instincts with a stunning volley from a narrow angle that crashed in off the far post.
They nearly added another on 69 minutes when midfielder Danny Hollands turned neatly on the penalty spot before forcing a good low save from Brain with a powerful drive.
However, Brain was found wanting a minute later when Bradbury again ghosted on to a Jeff Goulding cross to the far post.
The former striker powered a low drive that the keeper could only half parry and was too late to claw back as it inched agonisingly over the line.
Macclesfield had few chances to get back into the game but they went close on 85 minutes with a rising free-kick from Lee Bell that was easily saved by Jalal.
Then, on 89 minutes John Rooney, the brother of Wayne, curled a 20-yard drive inches over the crossbar.