He rolled the ball into an empty net after a strong run by fellow replacement Paul Connor to leave Brighton still looking for their first home league win of the campaign.
Cheltenham's improbable comeback upstaged Robbie Savage's arrival at Brighton on a month's loan from Derby.
The controversial former Wales international midfielder showed his quality at times but collected a late booking and was taken off shortly before Gallinagh struck.
The result was rough on Brighton striker Glenn Murray, who scored a hat-trick to take his tally to six goals in the last three games.
The former Rochdale marksman gave the home side a perfect start, heading in a cross from David Livermore in the first minute.
Cheltenham were level a minute later, on-loan Bristol City winger Scott Murray converting a cross by Stuart Fleetwood from close range.
Glenn Murray restored Brighton's advantage only seven minutes into the contest, rounding the Cheltenham keeper after captain Nicky Forster had set him up.
His Cheltenham name-sake levelled again in first-half stoppage time with an unstoppable 25-yard right-foot volley.
Brighton's Murray completed his hat-trick two minutes after the restart with another header from an inviting cross by impressive midfielder Kevin Thornton, making his home debut on loan from Coventry.
Cheltenham's hopes seemed dead and buried when teenager Josh Payne, borrowed from West Ham, was sent off for a second bookable offence five minutes from time.
But Martin Allen's battlers refused to be denied as Gallinagh's last-gasp strike earned them an unlikely share of the spoils.
It was another late setback for Brighton after letting in an equaliser six minutes into stoppage time in their previous match at Northampton Town.