Christian Panucci opened the scoring for Luciano Spalletti's team on the stroke of half-time and Alberto Aquilani doubled the advantage six minutes after the interval.
Substitute Simone Perrotta put the icing on the cake for the Eternal City giants in stoppage time.
Roma headed into the encounter in 17th spot in the standings following a dismal start to the campaign.
A 1-1 draw against Sampdoria and a 3-1 defeat at Palermo kicked off the domestic season and the poor form carried over to the Champions League with a shock 2-1 home defeat to competition debutants CFR Cluj in midweek.
Last term's Italian runners-up finally returned to winning ways on Saturday, although it could have been different had a seventh-minute shot from Reggina midfielder Luca Vigiani gone in instead of skimming the right-hand post.
Matteo Brighi had the hosts' first sight of goal seven minutes later but lashed his 25-yard shot over Andrea Campagnolo's crossbar.
Aquilani and Jeremy Menez then both tried their luck from a similar distance but to no avail.
Menez produced a fine low cross into the box following good work again by Aquilani just after the half-hour mark, but there were no Giallorossi forwards on hand to capitalise.
The deadlock was finally broken in first-half stoppage time when Panucci, who also netted against Cluj in midweek, fired into the bottom-right corner after Campagnolo had saved Rodrigo Taddei's initial effort.
Mirko Vucinic came close to doubling Roma's advantage three minutes after the break, only to be denied by a smart diving save by Campagnolo.
Three minutes later it was 2-0, however, when Aquilani smashing his shot under the bar from the edge of the area.
Aquilani had another blast from the same position just before the hour mark but this time his attempt flew over the bar.
France international Menez, making his first start for Roma following his 10million euro summer transfer from Monaco, continued to look dangerous and almost added a third midway through the second half but his shot was kept out by the sprawling Campagnolo.
Perrotta, who had been doubtful for the match with a muscular problem, was introduced as a 69th-minute replacement for Menez and appeared eager to make his mark.
The Italy midfielder drilled a shot against the post 14 minutes from time, only for the referee to pull play back for offside.
Bernardo Corradi came within inches of halving the deficit for Reggina in the 81st minute but his shot from the left flew just wide of the right-hand post.
Play soon returned to the other end, though, with defender Panucci looking to double his personal tally from a 25-yard shot but Campagnolo was equal to it.
The third goal did come, however, in the third minute of stoppage time, when Perrotta followed up to slot in from close range after the unlucky Campagnolo had kept out Francesco Totti's free-kick.
by espnstar.com
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