The home side dominated the first half and on-loan keeper Sam Johnstone was never stretched by the visitors on his home debut.
Middlesbrough played with a lone striker and their safety-first tactics paid off as they recorded another clean sheet.
They looked more menacing in the second half but were unable to find the net in a game in which both defences finished on top.
There was plenty of end-to-end action at the start although chances were at a premium.
Doncaster had a definite edge and grew in confidence as the half progressed to put the visitors under plenty of pressure.
Then Rovers were denied a penalty following loud appeals when Coppinger drove a 20-yard free-kick into the defensive wall in the 18th minute.
Defenders were in command and it was not until the 23rd minute that either keeper had a shot to save, Chris Brown sidefooting into Shay Given's hands after Richie Wellens and Billy Sharp had created the opening.
It was one-way traffic for a spell as Boro were pegged back in defence and Wellens fired over after a free-kick from James Husband had only been half-cleared.
Middlesbrough did not manage to land a shot on target for the first half and only forced one corner, in the 38th minute, which came to nothing.
But the visitors defended with confidence and Coppinger had another short deflected just before the interval as the score-sheet stayed blank at half-time.
Middlesbrough came into the game more in the second half and they had a great chance to break the deadlock in the 53rd minute.
Grant Leadbitter produced a superb through-ball for Emmanuel Ledesma to race on to but he placed his shot just wide of the mark.
The game was more open after the break and Coppinger had a fierce angled drive saved at the second attempt by Given in the 57th minute.
Johnstone had his first save to make three minutes later when he held on to a header from Curtis Main at the near post following good work by Ledesma.
Sharp created the best chance of the match moments later when he crossed the ball to the unmarked Brown, who fired over the top from close range.
Both sides went close in a frantic finish, with George Friend and substitute Kei Kamara not far off the mark for the visitors while Brown had a volley cleared off the line in injury time.
- Sports & Recreation
- James Coppinger
- Sam Johnstone
- Richie Wellens