Kris Doolan had given Alan Archibald's team an early lead with a precise finish from an improbable angle but they were pegged back three minutes before half-time after MacLean swept the ball home.
Neither team came into the match enjoying much luck in the league of late, with St Johnstone four games without a victory and Thistle three.
And a basic lack of quality from both sets of attackers in the final third ultimately ensured their wait would continue.
Both sides had decent opportunities to work the ball into dangerous territory but the second half failed to bring a winner.
The home side endured a nightmare start as Thistle struck after six minutes.
The Jags celebrations were a painful sight for the home side, and more so Anderson as his fall resulted in a sore-looking wrist injury and the centre-half was replaced immediately by Gary Miller as he walked off with agony etched across his face.
Doolan could have had a second soon after but failed to get a firm touch on Aaron Taylor-Sinclair's cross with his header while Dave Mackay's free-kick at the other end was pushed away by Paul Gallacher on the quarter hour.
Despite trailing, the home side refused to be over-rushed and some of their passing exchanges were impressive to watch.
By the same token, Thistle remained happy to hit St Johnstone on the counter and it proved an effective ploy as Mannus was forced to save after another swift attack saw Kallum Higginbotham fire a low drive at the Northern Irishman 32 minutes in.
Another Doolan header failed to beat Mannus from Higginbotham's centre just before the break but it was Saints who grabbed the equaliser with three minutes left of the half.
MacLean and Patrick Cregg combined on the edge of the Partick box but the opportunity looked as if it had gone when the Irish midfielder opted against a first-time shot as he gave the ball back to MacLean.
The former Sheffield Wednesday and Aberdeen frontman worked half a yard of space before whipping a low shot into the corner of the net.
Gallacher - in for his first start as a Partick player - will be unhappy with his part after getting down in time to save, only to let the ball bounce under his wrist.
The goal was just what Saints needed and they nearly grabbed another seven minutes after the restart as Stevie May's shot looked destined for the bottom corner before Stephen O'Donnell slid in to clear for the visitors, while Gallacher shook off his rustiness to do better with Chris Millar's 18-yard strike after 63 minutes, diving to his right to send the ball out for a corner.
However, the former Scotland stopper was unconvincing again as he just about managed to turn away May's low shot following a swift break away by St Johnstone.
Doolan and James Craigen worked a clever opening after the goalscorer's dummy left the Saints back four flat-footed but he failed to grab a second after wasting substitute Craigen's through ball.
Mackay should have won it for his side with just 60 seconds left when he darted on to MacLean's cut back but his finish was tame and easily gathered by Gallacher.