Wilfried Nancy was announced as the new Celtic boss prior to kick-off on Wednesday night at Celtic Park and Martin O'Neill's final match in caretaker charge ended in victory thanks to Maeda's 11th-minute header.
"It wasn't the most flamboyant of victories. But three points on the board keeps it going," said O'Neill.
Victory for the Hoops means they move level on points with Hearts, who stay top of the table on goal difference after drawing 1-1 with Kilmarnock at Tynecastle.
Lawrence Shankland fired the hosts in front but Bruce Anderson's 90th-minute equaliser ensured Hearts made it four games without a victory.
Nedim Bajrami's added-time penalty rescued fourth-placed Rangers a point in a 2-2 draw against Dundee United.
Former Sydney FC and Western Sydney forward Zac Sapsford put the hosts ahead at Tannadice, but Jayden Meghoma levelled with his first Rangers goal since joining on-loan from Brentford.
United took advantage of their first real chance when Sapsford sped away from Gers defender Emmanuel Fernandez on the touchline to chase a Lucas Stephenson pass and raced 40 yards straight into the penalty area before confidently chipping diving Gers keeper Jack Butland on the angle.
Amar Fatah fired the home side back in front and following a foul on Max Aarons in the area, Rangers were awarded a penalty which Bajrami blasted home in the eighth minute of time added on.
"On the weekend, we didn't create a lot of chances - but tonight we had chances for maybe four games," Rangers manager Danny Rohl said.
"But ... on Sunday we got a clean sheet. Tonight we didn't have.
"If we could bring the two together, the clean sheet along with the style we played with tonight - we'll get a lot of points in the future."
Elsewhere, Richard King also struck late for St Mirren to snatch a 3-3 draw at Aberdeen and Falkirk drew 0-0 with Motherwell.
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