Russia's world number three Sharapova, the defending champion, beat French qualifier Caroline Garcia 6-3 6-2 in their second-round clash.
Sharapova broke twice early on, and while Garcia did break back once, the revival was short-lived as the Russian won back-to-back games for an unassailable first set lead.
The second set was on serve until Sharapova broke to go 4-2 up, before breaking again as Garcia went long.
The victory took one hour and 16 minutes and sets up a third-round match with either Sloane Stephens or Klara Zakopalova.
Sharapova's last match against Garcia was at the French Open two years ago when the Russian found herself 6-3 4-1 down before rallying for a three-set victory.
"I was quite happy with the way I played because my opponent had played a few matches already, so she's been able to get into that match atmosphere," Sharapova said.
"Sometimes that's a benefit. I wanted to start really strong. I had a really tough match against her in our previous encounter, so I really wanted to start better this time, as opposed to the way I started against her last time."
Things did not go so well for Russia's 12th seed Maria Kirilenko, who withdrew injured in the first set of her first-round match with compatriot Ekaterina Bychkova.
Second seed Serena Williams was also given a first-round bye and was similarly imperious in victory, beating Daria Gavrilova of Russia 6-2 6-1 to cruise through.
Williams will take the world number one spot if she reaches the semi-finals in Doha.
The 15-times Grand Slam winner has not topped the rankings since October 2010, but is close to returning to the pinnacle having claimed last year's Wimbledon and US Open titles.
Williams, who has now won 57 of her last 60 matches, broke Gavrilova in the sixth game of the first set and then raced away with the match in 54 minutes.
Question marks hung over the world number two's fitness heading into the event after she lost in the Australian Open quarter-final last month while suffering with back and ankle injuries.
"Mostly I've just been trying to play smoothly and avoid problems, and just do the things I've been working on," Williams said on the WTA website.
"Physically I'm feeling better, and hopefully I can stay on that level. Let's go onto the next round now."
Also in the second round, fifth seed Angelique Kerber was knocked out, losing 6-1 6-2 to fellow German Mona Barthel.
British number two Robson suffered a 6-4 6-1 defeat to Slovakia’s Daniela Hantuchova to go out in the first round.
Hantuchova broke to 5-3 in the first set, before dominating the second to win in just over an hour and a quarter.
World number 45 Robson is ranked 30 places above Hantuchova, but may have been feeling the effects of her Fed Cup heroics last week.
Both Robson and British number one Heather Watson won all of their matches as Great Britain beat Bulgaria, Portugal, Hungary and Bosnia to move into the World Group II play-offs.
Other big names to progress were ninth seed Marion Bartoli, who beat former French Open champion Francesca Schiavone 7-6(5) 6-3, and 15th seed Roberta Vinci, whose opponent Yanina Wickmayer retired injured while 2-6 1-2 down.
Qatar Open second round results:
2-Serena Williams (US) beat Daria Gavrilova (Russia) 6-2 6-1
3-Maria Sharapova (Russia) beat Caroline Garcia (France) 6-3 6-2
Mona Barthel (Germany) beat 5-Angelique Kerber (Germany) 6-1 6-2
Qatar Open first round results (day two):
Ekaterina Bychkova (Russia) beat 12-Maria Kirilenko (Russia) 3-0 (Kirilenko retired)
Daniela Hantuchova (Slovakia) beat Laura Robson (Britain) 6-4 6-1
Timea Babos (Hungary) beat Heidi El Tabakh (Canada) 6-2 6-3
16-Sloane Stephens (US) beat Anna Tatishvili (Georgia) 6-2 6-2
9-Marion Bartoli (France) beat Francesca Schiavone (Italy) 7-6(5) 6-3
Romina Oprandi (Switzerland) beat Tsvetana Pironkova (Bulgaria) 7-6(2) 7-5
Monica Niculescu (Romania) beat Jelena Jankovic (Serbia) 6-4 6-1
Klara Zakopalova (Czech Republic) beat Varvara Lepchenko (US) 7-6(8) 3-0 (Lepchenko retired)
15-Roberta Vinci (Italy) beat Yanina Wickmayer (Belgium) 6-2 2-1 (Wickmayer retired)
Ekaterina Makarova (Russia) beat Carla Suarez Navarro (Spain) 6-1 6-2
17-Lucie Safarova (Czech Republic) beat Eleni Daniilidou (Greece) 6-2 6-3
11-Nadia Petrova (Russia) beat Andrea Hlavackova (Czech Republic) 6-2 6-3
Hsieh Su-Wei (Taiwan) beat Tadeja Majeric (Slovenia) 6-4 6-4
Sorana Cirstea (Romania) beat Ons Jabeur (Tunisia) 2-6 6-3 6-0
Christina Mchale (U.) beat Vera Dushevina (Russia) 6-1 6-2
Urszula Radwanska (Poland) beat Nadiya Kichenok (Ukraine) 6-1 6-0