The home side attacked Partick's defence early on and started as the stronger team.
On eight minutes, Inverness debutant Ben Greenhalgh came close to giving his side the lead with a volley from an acute angle, but he could only strike the post.
The visitors took the lead on 20 minutes when Doolan latched onto James Craigen's cross to make it 1-0.
Craigen then had a huge chance to double Partick's lead on 32 minutes, but he could only curl his effort over the bar, despite being in plenty of space on the edge of the box.
Partick continued to trouble Inverness with their swift counter-attacks, with Stephen O'Donnell coming close with a 30-yard drive on 35 minutes.
Inverness started the second half well and soon found an equaliser on 46 minutes through Gary Warren, who headed home a set piece to make it 1-1.
Greenhalgh threatened on 61 minutes when his cross from the left forced the goalkeeper to tip the ball over the bar.
Partick regained the lead on 82 minutes when goalkeeper Dean Brill dropped a cross, allowing Doolan to grab his second of the game from two yards out.
Doolan almost grabbed a hat-trick on 87 minutes, but he just could not connect with a cross from the left to make it three.