Captain Steven Davis struck the opener on 15 minutes when he steered home a shot from Nikica Jelavic's pass before a second from the home side arrived a minute into two added on for stoppages when Aberdeen goalkeeper David Gonzalez spilled a free-kick and Naismith followed up to net from four yards.
The result was harsh on Craig Brown's visiting team, who enjoyed as much possession as the SPL champions without converting the chances that came their way.
Their best moment of the game arrived early in the second period when Allan McGregor failed to hold Scott Vernon's dipping effort from distance, but former Rangers player Richard Foster somehow managed to loop a header off the bar from eight yards out.
It was an unconvincing performance from Rangers as Ally McCoist completed his first win at Ibrox as the Glasgow club's manager, but they will take the three points in a week when they were emptied out of the Europa League qualifying stage by the unfashionable Maribor of Slovenia.
Rangers are ahead of Motherwell - who won 4-2 at Dunfermline Athletic on Saturday - on goal difference at the top of the SPL on 13 points with city rivals Celtic a point behind in third place after their 2-0 win over St Mirren in Paisley earlier in the day.
Gary Hooper scored twice in the opening 12 minutes as Celtic recovered from their European disappointment with a 2-0 SPL win at St Mirren.
Celtic - still reeling after crashing out of the Europa League after a 3-1 loss to Swiss side Sion on Thursday - opened the scoring on six mnutes when Hooper combined delightfully with Anthony Stokes to slip the ball beyond the outstanding St Mirren goalkeeper Craig Samson from close range.
Paul McGowan gave the ball away needlessly on 12 minutes as Hooper strode forward unmarked to thrash the ball beyond the exposed Samson to finish off the match as a contest.
Celtic defender Kelvin Wilson almost nodded beyond his own goalkeeper Fraser Forster in the second period, but despite the game nature of a St Mirren side that battled manfully and were easy on the eye, Celtic squandered several clear-cut chances to increase their lead.
Samson was the busier keeper in making fine stops to deny Ki Sung-Yueng and James Forrest while Stokes had a goal wrongly disallowed for a foul on Marc McAusland in the opening moments.
Ryan Stevenson and Andy Webster were on target as Hearts inflicted Hibernian's third consecutive SPL defeat with a 2-0 win that keeps their rivals bottom of the table.
Hibs struggled to cope with the attacking play of Jamie Hamill and Stevenson down the right and the pair combined to open the scoring six minutes before the break.
Webster headed Hamill's 68th-minute corner over the line despite Akpo Sodje's attempts to clear as Hearts dominated the second period.
There is a break from domestic action next weekend due to Scotland's Euro 2012 qualifier with Czech Republic at Hampden Park.
Rangers visit Dundee United on September 10 with Celtic hosting Motherwell on the same day before the Glasgow pair meet in the first derby of the season at Ibrox on September 18.
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