The goal was the Ugandan's first for almost six months and manager Jefferies was less than impressed by his second-half display before he nodded home Ryan Stevenson's inviting cross.
"I didn't think big Obua started the second half as well as I wanted so I was very close to subbing him," said Jefferies after masterminding Hearts' second straight win.
"Ryan Stevenson's made a great run and shown great composure because a lot of people would have played the ball in.
"But he took a touch, waited for the support and David just met it sweetly."
Substitute David Templeton was then gifted his first Hearts goal following a horrendous blunder from Brian Easton to settle a Tynecastle match that was as tight as Jefferies had anticipated.
"It was all about the result today," he said.
"The surface is bobbly and bumpy and it was never going to be a classic."
Hamilton's only real chance arrived shortly before Obua scored, with Flavio Paixao forcing a great stop by Marian Kello after a quick breakaway.
Otherwise, the visitors were set up to frustrate.
Jefferies said: "They're dogged, they sit in, they flood the middle of the park, especially when you get the ball.
"They won recently up at Tannadice, so that's what I told the players they were going to face today.
"It was all about the first goal today and I think the turning point was when Marian had a great save at 0-0 and we go straight up the park and score."
The result cemented Hearts' hold on sixth place after Aberdeen were beaten by Falkirk.
"Great weekend," Jefferies said.
"Somebody just told me that's the first time that we've won by two clear goals this year, so that's another plus for us."
Jefferies, who lost Suso Santana to a thigh knock early in the second half, singled out much-maligned defender Dawid Kucharski for special praise.
He also applauded a 10-minute cameo from Laryea Kingston, who took to the field to a mixture of cheers and jeers.
"He had a lively 10 minutes, he had a couple of pops at goal," said Jefferies, who promised the Ghana midfielder a fresh start after succeeding Csaba Laszlo as manager.
"Hopefully we can see that he's going to give his lot for us."
Kingston's commitment to Hearts has been called into question in the past but Jefferies hopes to help him win over his critics.
"I'll be kicking his backside in training to make sure he does that," he said.
The new Hearts boss also reiterated his intention to draw up a strict code of conduct on the day it emerged the three Jambos stars fined by the club for their post-match behaviour during December's defeat at Hamilton had been let off the hook by an administration blunder.
Opposite number Billy Reid agreed with Jefferies that the first goal was vital today.
"I don't think we deserved to take something out of the game," he admitted.
"They scored two goals and if you score two goals, you deserve to win the game.
"I certainly don't think there was anything in the game.
"I never felt under real pressure; they'll probably say the same.
"First real chance is probably Flavio Paixao being put through one on one with the goalkeeper.
"He smashed it - decent strike - the goalie's made good save, and they've gone up the park and scored a goal.
"I thought the first goal was always going to win it for either team and unfortunately it was Hearts who got it."