The Silkmen had the first sight of goal after just five minutes when Neil Mackenzie slipped the ball into the middle from deep on the right flank for Matt Tipton to hit first time, but the shot flew straight at Willy Gueret in the home goal.
The Swans responded with a break from Andy Robinson but Thorpe's shot lacked power and Alan Fettis had little difficulty in gathering.
Swansea took the lead in the 25th minute with a well-worked set-piece. Robinson knocked over a free-kick and Thorpe rose high to head firmly into the back of the net.
Robinson was again the provider as Swansea doubled their lead in the 32nd minute, when Macclesfield defender Michael Welch missed his throughball and Connor raced in to fire beyond Fettis and into the corner of the net.
The Swans were now well on top and a Kristian O'Leary shot brought a flying save from Fettis as the first half drew to a close.
Connor should have killed off the game six minutes into the second half when a slip by David Morley gave the former Rochdale striker a clear run on goal, but with only the keeper to beat he screwed his shot wide of the far post.
The Silkmen brought on all three substitutes but they were still made to play second fiddle to a Swansea side eager to push themselves back into the race for automatic promotion.
The visitors' cause was finally lost when they went down to ten men in the 81st minute when striker Jon Parkin was dismissed after tangling with Izzy Iriekpen.
Parkin had a running battle with the home defence all through the match and it was no surprise when he received his marching orders.
The visitors tried hard for a consolation goal but the Swans' defence held firm to close the gap on the clubs at the top of the table.