Two goals from in-form striker Andrew Waterworth ensured that league leaders Linfield picked up their seventh consecutive Premiership win.
The ex-Glens forward went close with a left-foot curler wide of the post and a right-foot effort which was well saved by visiting goalkeeper Gareth Buchanan.
Waterworth spun and rifled home into the bottom corner in the 40th minute.
Matthew Tipton set up his strike partner for the second, Waterworth scoring with a near-post header on 58.
The Blues are four points ahead of the chasing pack, although second-placed Portadown have a chance to close that gap when they face Glenavon on Monday night.
"There is always pressure at this club but the players are working tremendously hard and deserve a massive amount of credit," said Blues' boss David Jeffrey.
Darren Murphy's Swifts drop to seventh.