The Blues sealed the three points after edging a second half that produced five goals.
George Hirst (50 minutes – penalty) and Michael Jacobs (68) handed the home side a 2-0 lead, before Teddy Bishop (70) and substitute Ben House (78) got the Imps back on level terms.
However, Pompey substitute Ronan Curtis restored the Blues’ advantage on 82 minutes when he made the most of goalkeeper Jordan Wright’s inability to hang on to Sean Raggett’s drilled effort to bag his eighth goal of the season.
10. George Hirst - 7
Not at Rotherham heights, yet scored a penalty and put plenty into it. Photo: The News
11. Aiden O'Brien - 7
(Replaced by Ronan Curtis on 70 minutes): Wasted glorious second-half chance, but energetic and clever on the ball as ever. Photo: JPIMedia
12. Ryan Tunnicliffe - 7
(Replaced Joe Morrell on 12 minutes): Took a while to settle down, but better in second half. Photo: JPIMedia