After Fleetwood's Bobby Grant put a 25-yard curler just wide, the hosts went ahead as Alex Gilbey picked up a loose ball and drilled home a low shot.
Jonsson scored his second goal of the season to equalise with a thunderbolt into the top corner.
Fleetwood had a late chance to win it but Nick Haughton curled his shot wide.
The hosts also went close but Fleetwood keeper Chris Maxwell denied George Moncur.
Colchester remain in the relegation places in 22nd, still five points behind Fleetwood in 20th.
Eggert Jonsson's second-half equaliser edged Fleetwood a point clear of the League One relegation zone with a point at fellow strugglers Colchester United.