The Finish goalkeeper denied both Benni McCarthy and Jason Roberts in a frantic final three minutes, which also saw Trotters captain Kevin Nolan dismissed, after Ivan Campo had scored the only goal of the game.
In contradiction to Rafel Benitez's rotation policy, both managers named unchanged teams following 2-1 away victories last time out - Poland's Wisla Krakow on Thursday night for Rovers and Newcastle last Sunday for Bolton.
After a slow start, which wasn't helped by a head injury to Abdoulaye Faye, the game sprung into life on the quarter hour.
From Morten Gamst Pedersen's in-swinging corner, the unmarked Zurab Khizanishvili headed the ball back across goal for defensive partner Andre Ooijer, but the Dutchman's header from virtually underneath the bar was deflected over for another corner.
Four minutes later, following a foul by Gary Speed on Robbie Savage, Rovers' Welshman picked himself up before unleashing a trademark right-foot curler, which Jaaskelainen had to tip clear from the top corner of the net.
Straight up the other end, Nicolas Anelka skipped past Lucas Neill down the right, before playing in the unmarked El Hadji Diouf in the centre, but the Senegalese striker's tame shot was comfortable for Brad Friedel.
A minute later and the same duo combined from a similar situation. Again Anelka broke down the right, his cross found Diouf, but the former Liverpool man's diving header crashed back off the post.
Pedersen and Tugay warmed Jaaskelainen's gloves with long-range strikes, before Rovers again threatened from successive corner kicks.
From the first, the ball dropped to Shabani Nonda and only a last-ditch tackle prevented a certain goal, before Pedersen again picked out the unmarked Khizanishvili at the back post. The Georgian's downward header took a slight deflection past Jaaskelainen and although it appeared to cross the line, Speed hooked it clear and referee Mike Dean waved play on.
Rovers had the last word of a thrilling half, as David Bentley shot straight into the arms of Jaaskelainen after being played clean through by Brett Emerton, before the Australian full-back was sent crashing to the ground by Diouf inside the box - but again the Cheshire official remained unmoved.
The high-tempo continued after the break with chances being created at either end. On 53 minutes, Neill played in McCarthy inside the box, the South African star turned brilliantly past Tal Ben Haim, but his goalbound effort was palmed away by Jaaskelainen.
The saved proved crucial, as just nine minutes later the visitors took the lead. Bentley gave a needless corner away on the right and from Diouf's delivery, Campo rose highest to powerfully head home from six yards.
But the real drama was yet to come. In the 87th minute, Roberts was caught late by fellow substitute Quinton Fortune on the right-hand edge of the box and the referee was left with no option but to point to the spot. Up stepped McCarthy, but Jaaskelainen guessed correctly and made the save.
Two minutes later and again Roberts was brought down after being sandwiched between two players and on this occasion the former Wigan man picked himself up to take aim, only for Jaaskelainen to pull off an almost identical save.
Nolan was shown a straight red card in the chaos that followed, as third-place Bolton held on for the points.