The USA star struck early on to extend the Ibrox team’s advantage over Celtic in the league to 13 points ahead of the Parkhead side’s game at Hibs tomorrow.
But his winner only told half the story on a tense afternoon in Govan as Accies dominated for large spells and were unlucky not to take something from the game.
It seemed they had equalised in the closing stages through James McArthur but his effort was flagged offside and disallowed.
On reflection, it was the wrong decision and that call gave Gers an undeserved boost as they hung on to take the points.
Now they face Aberdeen on Wednesday knowing victory in that fixture will take them that little bit closer to the silverware again.
But boss Walter Smith will be looking for a far better showing against the Dons from his side, which once again failed to deliver the type of performance it is capable of.
Smith made just one change to the team which crashed to a shock 4-1 defeat against St Johnstone at McDiarmid Park.
Clearly unhappy with Kevin Thomson’s performance in Perth, the manager dropped him to the bench and Edu replaced him.
Otherwise, it was the same team which had been so disappointing against Derek McInnes’ side which lined up against Accies.
And that meant Kris Boyd, without a goal from open play in nine games, was given the nod to start up front alongside Kenny Miller.
Steven Naismith also made the first XI, with Danny Wilson continuing at the back in the absence of Madjid Bougherra and Kirk Broadfoot.
Rangers were eager to get an early goal after starting games slowly in recent weeks and after Kenny Miller’s near-post effort was saved, it was Edu who gave them a lead.
The American had gone so close to netting when he struck the base of the post from 25 yards following good build-up play involved Steven Davis and Lee McCulloch.
And Edu got what he deserved just seconds later on 10 minutes when he connected with a low Miller cross and stroked into the back of the net with great composure.
Gers did have opportunities to add to their lead, with Boyd’s 18-yard shot deflected just wide and Davis shooting into the side netting with his left foot.
But, by and large, it was Accies who made most of the running for the rest of the first half and they were unfortunate not to be level at the interval.
Flavio Paixao should really have hit the target after being set up by Simon Mensing but didn’t.
And it took a wonderful tip over the crossbar from Allan McGregor to deny the Portuguese striker when he curled towards the top corner from the edge of the area.
Dougie Imrie also had an opportunity for the away side but he nodded well over after a good cross came in from Brian Easton on the left.
The Lanarkshire outfit was playing some good football and passing the ball about with great confidence.
And as the midway point approached and the Light Blues became more agitated, they struggled more and more to take charge of the game.
Hamilton were the side dictating much of the play and although Naismith was denied just before the interval, a second home goal at that point would have flattered Smith’s men.
As the players made their way off at the break, the animated reaction of some Rangers players suggested the midweek result up the A9 still wasn’t out of their system.
Indeed, it was no surprise they used every minute of the pause in play to discuss their performance and set about improving it.
The hosts got better initially after the restart and captain David Weir headed over the bar then Miller cleared the upright after a neat one-two between him and Boyd.
Davis also intercepted after a poor pass by visiting defender Mark McLaughlin but Thomas Cerny spread himself really well to save from the Northern Ireland star.
Almost immediately, Hamilton broke upfield and might have leveled had Imrie not been unsighted when he shot through a ruck of bodies and steered well off target.
For all that Rangers had lifted themselves a little, there was still just one goal between the sides and Accies took great hope from that.
As the second period wore on, a similar pattern developed to what was seen in the first 45 minutes and the away team settled into a rhythm again.
Smith tried to combat that by throwing on Kyle Lafferty for the ineffective Boyd and his first contribution was a decent curled effort beyond the far post.
Davis released Edu as Gers tried to lift themselves from their slumber and the ex-Toronto man made his way into the box but a crucial tackle denied him a shooting chance.
Back came Hamilton, who had plenty of pressure without really troubling McGregor much.
That’s ultimately what cost them and if they’d had a cutting edge and a better final pass, they’d have taken something from this game.
Naismith headed past the post from a Davis cross and Lee McCulloch’s drive was deflected away from goal from 30 yards as Rangers came briefly upfield.
At the other end, substitute Joel Thomas tried his luck from distance but while he was on target, his attempt to score was relatively tame.
With the clock ticking down, the onus was on Rangers to finish their opponents off and Miller got into a great position to do that.
But after Davis was blocked and set up the striker from the rebound, he lifted the ball over the bar when it seemed easier to put it in the net.
Hamilton knew time was running out for them and it seemed they had finally levelled when McArthur ghosted in behind the defence to net with his thigh late on.
But the jubilant celebrations on the away bench were cut short as far side linesman Steven Craven flagged for offside and it was a huge let off for Gers.
TV replays showed the midfielder had come from a deep position and it seemed to be the wrong call from referee Stevie O’Reilly’s assistant.
After Rangers had failed to heed the warning when Dundee United had a goal ruled out for the same reason 10 days previously, there was a nervy ending to this game.
There perhaps shouldn’t have been, however, as Nacho Novo broke the offside trap and shot straight at Cerny when Lafferty was in space for a tap in.
When the final whistle blew, the muted applause from the home crowd reflected how much of a stuttering performance the Light Blues had given.
Regardless, they had done just enough to win 1-0 and sneak three points and that’s what matters most as they eye a second successive title.