Swansea extended their unbeaten run to four games and leapfrogged opponents Bradford in the table thanks to Andy Robinson's solitary strike.
Striker Adebayo Akinfenwa had the best opportunity of the first half but Bradford goalkeeper Donovan Ricketts tipped his goal-bound effort wide of the target.
The visitors then suffered an injury blow in stoppage-time when Dean Windass was forced off and replaced by David Graham.
Swansea enjoyed the majority of possession in the second half and they were rewarded for their play when Robinson wriggled free of the City defence to fire a left-foot shot into the net from six yards.
The hosts continued to push for a second goal and Akinfenwa had a chance five minutes from time only to see Ricketts deny him with a fine save.
Leon Knight could have doubled the Swans' lead seconds before the whistle but Ricketts was again alert to save the 25-yard strike.
Swansea manager Kenny Jackett hailed his side's 1-0 home win over Bradford as their best display of the season "by some way".
A strike by substitute Andy Robinson gave the Swans a deserved victory over a well-drilled Bantams outfit.
Coming on for Leon Britton midway through the second half he only took five minutes before shooting his side's winner with a left-footed shot following goalmouth scramble.
"That was the best performance at home this season by a considerable way," said a delighted Jackett.
"We were looking to score more goals, but at least created a number of chances against a very good Bradford side.
"We have given away possession too easily in previous matches so I brought in Bayo (Akinfenwa) and he held up well and also worked his way into shooting off opportunities. I'm sure that he will soon be regularly on the score sheet.
"We have started the season slowly, but we were a little more like the real us."
Despite the home side's early domination, it was the Bantams who had the first goalscoring opportunities.
Jermaine Johnson flashed a shot over the home crossbar and then veteran Dean Windass was worked through the middle only for Swansea goalkeeper Willy Gueret to come out bravely and block.
Bradford's luck seemed to desert them when Windass was forced off with a foot injury on the stroke of half time.
"Our rhythm was broken when Dean left the field," said disappointed Bradford boss Colin Todd.
"But we had several opportunities to score in the first half and had we taken our chances it may have been a different story.
"I thought we had weathered the storm after their good start, but they are a side who have a spent a lot of money while I have to get by on loan players."
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