The Uruguayan, who moved on loan from Southampton in January, headed in the first in the 24th minute and added a fortuitous second 10 minutes after half-time to take his tally in a Boro shirt to three.
Ramirez was on hand to make Wolves - watched by just 291 away fans because the majority boycotted the trip to Riverside to protest over ticket prices and Sky TV's rescheduling of games - wait for a first win on Teesside since 1951, even though Middlesbrough defender Ben Gibson headed into his own net in the final minute.
Middlesbrough never looked like letting it slip and they capitalised on third-placed Hull's defeat at Birmingham on Thursday
Aitor Karanka's side are two clear of Burnley, who play Blackburn on Saturday.
The victory was achieved without Stewart Downing, who was one of five changes to the team which lost at Blackburn in midweek, when Karanka's frustrations suggested he would mix things up.
And he did, with the sight of the £7m former England winger's name among the substitutes telling after an ineffective spell of form.
Downing had not been left out since October, when he emerged as a second-half substitute to inspire Middlesbrough to a 3-1 win at Molineux when they were trailing by a goal.
That was when Wolves had hopes of a play-off place, but last weekend's victory over Derby was their first in eight matches; form not helped by the departure of Benik Afobe to Bournemouth in January.
Ramirez, who had been unfortunate to lose his place at Blackburn, was one of Middlesbrough's key signings that month and he put Middlesbrough ahead midway through the half.
When his free-kick from the left was cleared, he made his way unmarked to the back post to meet a delivery back into the box from Adam Clayton before heading low past goalkeeper Carl Ikeme.
After that Wolves struggled to make inroads on the Middlesbrough goal, even though the best of the home side's work was done outside of the penalty areas with Clayton, Adam Forshaw and Ramirez the key men.
Rhodes, without a goal to his name at the Riverside so far, looked as if he had would increase the lead 30 seconds into the second half when he glanced a header from Adomah's cross towards goal
Ikeme, who had a spell on loan with Middlesbrough earlier in his career, brilliantly tipped over.
Middlesbrough did not have to wait long for the extra goal cushion
This time, after Friend's pass dropped into his path, Ramirez's cross flicked off the shin of Danny Batth and dropped inside Ikeme's far post.
Dimi Konstantopoulos, the home side's keeper, made a second-half stop to thwart Joe Mason but Rhodes could have added a third had it not been for Ikeme regularly stopping him.
Wolves did pull one back in the final minute when Gibson inadvertently glanced a header into the top corner from Matt Doherty's cross, but Middlesbrough had already done enough to win.
Source : PA
Source: PA