David Nugent had hit a post for the visitors, before the home team netted the opening goal against the run of play when defender Matthew Bates got on the end of a Barry Robson corner to score his first goal of the season.
Boro were 2-0 up just before the break when Robson powered home a penalty after Joel Ward had felled Scott McDonald in the box.
David Nugent pulled a goal back for Pompey in the second half before Boro's Robson was sent off for elbowing Aaron Mokoena in the penalty area and Liam Lawrence equalised from the spot.
Strachan decided to risk Kevin Thomson from the start after his apparent recovery from a fractured fibula, but the former Rangers man lasted only eight minutes following a challenge with Michael Brown.
Pompey, who were searching for their first away points of the season, had made the better start, nearly taking the lead on 13 minutes when Nugent shot against the post and Lawrence, following up, fired over from 12 yards.
Robson and then Lawrence, who was running the show in the early stages, threatened from long range for their respective sides.
The Teeside club then took the lead totally against the run of play on 29 minutes. After Ashdown had saved from Kris Boyd, the resulting corner from Robson was not cleared by the Portsmouth defence and Bates smashed the ball home from 10 yards out.
Middlesbrough, who were after their fourth consecutive home win, then went 2-0 up three minutes before half-time. A cross from Gary O'Neil found Ward out of position and in his attempt to clear he brought down McDonald, referee Rob Shoebridge pointing to the penalty spot. Robson stepped up and powered the ball into the top left-hand corner.
After the break Boro had a hat-trick of early chances, Boyd having the best one on 54 minutes as he flashed a shot just past the post having beaten the offside trap.
Pompey then pulled a goal back on the hour with Lawrence inevitably involved, Nugent heading in the on-loan Stoke man's cross.
Nugent curled an effort wide as Pompey attempted to crank up the pressure but Boro were still dangerous, with McDonald foiled by Ashdown.
The pressure on Middlesbrough then told as Portsmouth equalised on 87 minutes. Barry Robson inexplicably elbowed Aaron Mokoena inside the area, earning Robson a red card and Portsmouth a penalty that main man Lawrence calmly slotted home.